I know how it will work. Most likely nothing will happen. Egyptian regime is very fragile, and will not risk a foreign intervention while having to suppress monthly uprisings back home.
I think a war with Ethiopia would help the Egyptian regime, assuming it went well. And it probably would because Egypt's military is the strongest in the region minus Israel. The real question is what Sudan would do (probably lie down for the Egyptians).
The reason is the topography. Ethiopia has lots of mountains, like Switzerland and it is painful to attack.
Any foreign nation helping Ethiopia could mean disaster for Egypt.