I think Neqitan is on the right track. From what I've seen of Egyptian, the grammar is not unlike other Afro-Asiatics, even Semitics, despite not being in the same branch of the family. I would say it's probably firmly in the fusional category.
Well, I've skimmed some Ancient Egyptian dictionaries near me just for the fun, and so far the words resemble a very Semitic-like grammar (and that makes me believe they're from the same family). Haha, there were even some funny cognates with Arabic there and there I could recognize, like "m" standing for "what", just as Arabic mā (or maybe it's a coincidence...?).
Yeah, that is funny, isn't it? It's the same with Berber languages or something. I wonder what historical changes occurred for the languages to diverge that much.
Maybe it's not the exactly the same in Ancient Egyptian, but in Arabic, verb conjugations are either suffixes (-a, -tum, -tunna) or circumfixes (ta...īna, ’a...u) around a stem (agglutinative), and the stem derives from a root using a prefix (ta-, inta-, ista-) and some vowel playing (daras-drus) (prefixes and fusional).
The conjugations are fusional, not agglutinative because each affix expresses a number of meanings, not just one. For example هنّ hunna
is 3rd fem. plur. In Hungarian or Japanese, there would be a different suffix for each of these, right?