I have both of these models. I wouldn't normally have picked up the A2 except that it was $18.50 at a thrift store and I couldn't pass it up.
The A2e is an A2 with an added feature: the e designation means "eye control," and as far as I know this is the first Canon camera to have it. They added it on a couple of other EOS cameras, such as my Elan IIe, but it never became a standard feature. I don't believe it's on any of the digital EOS cameras at all.
Even without eye control, it was a very nice camera. EOS camera nomenclature for the Japan market was fairly clear: three digit numbers were entry-level, two-digit numbers were middle-tier (sometimes called "enthusiast" or "advanced amateur"), and one digit numbers were professional. The EOS-1 was always the top model, with other two-digit models slipping in just below it.
Both of mine came with the vertical grip accessory (shown on the bottom here, attached to the camera). It offered a second contoured handle, a second shutter button and finger-wheel so that if you are holding the camera sideways, you can easily hold the camera on its side and still get to the important controls.
For more information: Canon Camera Museum
Popular Photography camera test: Nov 1993
Camera manual: Orphan Cameras.com