you can Data recovery software such as Recuva or Easeus. There are many of these types of programs out there but they typically only work with drives that do not have mechanical issues. You need to ask yourself why your only copy of this data is on the backup drive?
Have you saved anything new on this external hard drive?
Actually, any new file on the same drive can rewrite the original data and make it gone permanently. So, you should take care.
However, no matter whether you rewrite it or not, you could try to recover your data back for free at the aid of free recovery software. This freeware was found by my friend as his WD external hard drive was mistakenly formatted by his little daughter. It fantastically recovered all his photos and files back. That’s why I recommend it to you.
In the future, you should learn to back up everything important on at least two different drives in case of similar problems.