Ah shit! I give up.
Had you searched you would have found out that YES any 4AGE 16V, 20V and 4AGZE will fit in your car.. you have a 4 "A" FE motor.. notice how all the other motors have an A in the name too.. this denotes that its an A series motor so any motor with that letter in it will fit your Corolla. The hardest part will be the wiring basically providing you bought a complete motor, if not have fun looking for whatever didn't come with the motor as the parts are hard to find. If you go for a GZE then you're looking at having to either source out a hood scoop from an AE92 GTZ in order to have the intercooler on the top.. if not you can fork out the money and have a front mounted intercooler instead.
So lets recap.. you got a 4
AFE so any of the following motors will fit.
16V Bigport 4
AGE - 88-89 Corolla GTS
16V Smallport 4
AGE - 90-91 Corolla GTS or Geo Prizm GSi
20V Silvertop 4
AGE - 92-94 AE101
20V Blacktop 4
AGE - 95-97 AE111
Supercharged Versions
16V 4
AGZE 88-89 MR2 SC (you will have to convert the tranny to FWD or use an AE92 GZE tranny)
16V 4
AGZE 88-89 AE92 GTZ
16V 4
AGZE 90-91 AE92 GTZ
16V 4
AGZE 92-97 AE101/AE111
OR you can do the less popular 3SGE/3SGTE swap, now notice how there's an S not an A on this motor.. that's right! that means this motor will require work to go in, mainly motor mounts and upgraded fuel system and FWD transmissions, but that's another ballpark.
As for being hard.. its only as hard as your wallet will let it be.

Hopes this helps.