Well...yes, it will. The E16i and GA16i have different trannies (Yes, there IS a difference, believe it or not), engine management wiring systems, emissions and fuel delivery systems between 'em. Unless you got some fairly deep pockets, you can do it...but I'd just keep 'er E16i.
The E16i is fairly inexpen$ive to rebuild, reliable as hell, economical, tough and responds well to aftermarket stuff. I'd get a crate engine or rebuild whatcha got. I think you'll be happy; God knows I LOVE my '87 E16i! This thing screams and gets 40mpg highway doing it.
Only caveat: The '87s use a 3-wire O2 sensor, which is $70 or so, NAPA; The '88 uses a single-wire O2 sensor that is about $20 (Damn engineers!)