You would need a mini PCIe one, usually they are on eBay. You will need the device, video card, power supply and a monitor to connect to the video card. Which would all add up to over $200, and it is not guaranteed to work with your system. Need to check with the eGPU vendor for system compatibility. You will also need to remove the WiFi card to use the mini PCIe slot so would need to buy a USB one.
For a video card for that system, a GT 1030 should be OK, cheaper and still decent for low spec gaming.