Formation of the empire is more to do with the expulsion of the Hyksos, and the contributions of the pharaohs in reestablishing Egyptian power.. Like Ahmose reconstructing buildings that had been damaged by the invasion, and the rise of militarism etc.
As far as I know administration of the empire is just a broad look at Egypt's internal and external policy, including trade, building works, relations with syria palestine and nubia.. Basically just how the empire was run.
Hope that helps, good luck tomorrow