In terms of "briefly learning" or "learning briefly" I'd say both are okay. But I suggest you don't write that you "enjoyed" learning about predicament. It suggests that you were happy to hear about the problem.
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AnonymousI enjoyed meeting you and learning briefly about the Academy's predicament.I am hopeful (not hopefull) things will work out.
Or:
I enjoyed meeting you and briefly learning about the Academy's predicament.I am hopeful (not hopefull) things will work out.