A novel maize variety designated PHH7E and seed, plants and plant parts thereof. Methods for producing a maize plant that comprise crossing maize variety PHH7E with another maize plant. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into PHH7E through backcross conversion and/or transformation, and to the maize seed, plant and plant part produced thereby. Hybrid maize seed, plant or plant part produced by crossing the variety PHH7E or a trait conversion of PHH7E with another maize variety. Inbred maize varieties derived from maize variety PHH7E, methods for producing other inbred maize varieties derived from maize variety PHH7E and the inbred maize varieties and their parts derived by the use of those methods.