I checked the National Park Service's "Soldiers and Sailors" system (online) & found two possibilities:

E.N. Crow, Co. A, 8th Battalion Georgia Infantry

Eli Crow Co. G, Cobb's Legion Infantry

If he and/or his widow applied for a pension from Georgia, it will reveal his unit, rank, etc. This can be found at the GA Archives building in Morrow, GA, along with his service records.