"The gap between the two countries keeps increasing."
"The gap between the two countries has continued increasing."
The verb "to keep", when it means "continue" does not sound good in the present perfect. I recommend using it in the present simple or the past simple, depending on your meaning.
"enormously" is an adverb related to size. You used it to modify a verb which describes motion, speed or change, and so it has no clear meaning. Perhaps you mean that the gap is now enormous, or that each month, year etc, the size of the increase was enormous.