Italy had nearly 3x the population and a modernized military and economy. They still lost. They ended up winning in the 2nd Italo-Ethiopian war, but the point is a war can be incredibly difficult to win, to the point where the amount gained from the is not worth the sacrifices made to win the war. Egypt would have to wage an all-out land invasion to win this war, and there's no guarantee that they would win.

Italy was fighting a colonial conflict against a nation on another conflict from their homeland. Egypt would be fighting a nation that borders them, with all the logistical advantages conferred by modern aircraft and vehicles.

It's a question of how many resources necessary to complete the task. Certain countries are too expensive to invade. Ethiopia may very well be one of these countries, with their mountain forts and defensive military philosophies.

Expense is relative. It was too expensive for the US to invade vietnam because making sure a country on the other side of the planet wasn't communist wasn't worth continued fighting. But for egypt, avoiding massive drought, famine, and economic turmoil is worth a lot more. Given a choice between having its citizens die in a war, versus having them die to water shortages, Any nation would make the decision to invade. Plus, Egypt doesn't need to occupy ethiopia like italy did. Egypt just needs to seize control of the nile, and maybe the Hala'ib Triangle for good measure.

Egypt's victory isn't guaranteed, of course, but given that they're essentially guaranteed to cause enough devestation in ethiopia that the whole point of building the dam (developing the country) would likely be obviated, at least in the near term, Ethiopia's only sensible decision would be to concede much of the water flow to egypt. In the long term, a better developed ethiopia might be able to re-negotiate from a position of strength, or at least parity, but that's not the modern scenario.