if you have a four-bay NAS with only two disks in it, the only way you'll be able to expand available capacity is by initializing the 18TB disk as a completely separate second volume in Storage Manager. There won't be any data redundancy or failure resilience. The second disk once initialized would appear in DSM as a separate volume, to be used as you see fit. You can't bridge or span the two disks in your configuration.
To add the drive and extend the capacity on the same volume in a SHR RAID, you would need at least three disks, two of which need to be of equal capacity. For example, two 18 TB and one 8 TB disk would give you 24 TB raw usable and 16 TB raw protection. Synology's RAID calculator is useful to visualise different combinations and compare RAID types.
https://www.synology.com/en-uk/support/RAID_calculator
SHR is just a brand name (Synology Hybrid RAID), which itself is just a combination of Linux tools to bootstrap some dynamic volume management and failure resilience on to an otherwise normal RAID array. However it's not without its own shortcomings, and I probably wouldn't use it again unless I knew I was going to expand my NAS capacity at a future time.
Internet forums debate SHR vs RAID and honestly, given my own practical experience on larger servers and storage configurations, I think I agree. RAID is adequate and possibly better for a storage system which will always have the same capacity - or will have capacity added by installing more disks in a second caddy attached to the first system, something most Synology devices can't do.
I would recommend always installing the maximum number of drives your NAS supports, and have them all the same capacity. That way you can use SHR-1 for 24 TB raw usable with one-disk failure tolerance, or SHR-2 with two-disk failure tolerance. Losing files from JBOD disks
hurts, though I appreciate NAS-grade disks also aren't cheap. (I bit the bullet and saved for a year to buy replacements)
So, er, why am I going on about all this? Hopefully it gives you some more ideas about what you could do in future, instead of just take the easy option of adding more disks to a box without any failure protection. I've done that enough times in my life to be burned more than once. Fortunately when two drives in my NAS started to fail this time around I had some failure tolerance. It always happens when you least want it to.
For what it's worth, if you decided to get / repurpose / shuck four smaller disks, to eventually replace with larger ones in future, it's not as daunting as it might initially seem.
I recently doubled the capacity on my DS918+ running DSM 6.2 by cloning the 4TB disks to new 8TB disks. I wasn't actually expecting it to work quite how I was hoping, but it did. And it saved a lot of time (probably 20-30 hours' worth) instead of just blindly following the Synology FAQs.
The Synology documentation advises that every time you replace a smaller disk with a larger one in an SHR array, you must insert the new empty disk, initialize it into the array then let the SHR (RAID) volume rebuild. This can take a
long time (potentially a day or more) if you have to wait four ties.
However, I decided to buy four larger drives then clone each of my four 4TB disks to new 8TB ones using a double-drive external caddy with integrated clone feature.
I replaced my disks one at a time, booting the NAS after swapping each 8TB drive to make sure it still worked. It did, and it could see the 8TB drives installed, but I was unable to expand the volume to use the new space.
At this point, I decided to bite the bullet and wipe one of my disks to rebuild the array. This took ~10 hours, but prior to beginning, DSM's Linux-based subsystem had very intelligently detected that 50% raw unused space was now available on the disk set, and offered to expand the volume to 100% available capacity.
Once it finished rebuilding the volume and onlined it, I investigated and could see that its LVM had created a second physical volume on each disk, added it to the volume group and then extended the logical volume to use all the newly available space, all without me having to do anything else. This meant I was able to double my DSM storage without having to rebuild the array four times, which is also beneficial for disk lifespan and means the process is finished far quicker.
I know that story's a little beyond the scope of your current situation, but I thought it worth mentioning to demonstrate the benefit of installing four smaller disks now, then planning the upgrade to larger disks once you have the means.
You can always clone one of the smaller disks to a larger disk and put it into the array in advance of upgrading the others, if money is a constraint. It'll still work, just behaving exactly like the smaller disk in terms of available capacity. However, building an SHR array like that will require you to rebuild the existing array or use new disks and transfer your data off beforehand. It may even be worth buying an 18TB external drive, copying your data off the NAS on to it, putting the other two disks in to a new blank SHR array, transferring your data off then shucking that 18TB disk to add to the NAS.
There's quite a few other possibilities too, the Synology user forums might give you some further inspiration. Although the DS416J is an older model than mine with a dual core ARM CPU, it still runs DSM. Underneath the skin it should have the same disk capabilities given it's still Linux.
Another alternative, if you have an old PC knocking about which is otherwise fine, and you want to 'end of life' your 2015 NAS: you might decide to put the new disk into a home-built TrueNAS, Unraid, or even an Xpenology machine. Xpenology is a very clever project - a custom bootloader and fork of DSM which lets you run Synology's software on just about any x86 hardware. That way you can save on the expensive Synology hardware but still use DSM, if you like the interface.
My next NAS won't be a Synology device, despite my NAS's convenience. Unless your storage needs are quite modest, you may find you eventually also outgrow any prebuilt NAS brand, unless you have tons of money to spend on their hardware and specific models of hard disk which are supported by them to guarantee full support should you have any problems.
For the moment, hope that's given you some ideas to what to do next. Please check back and let us know what you decide to do.