If he's black based, then he can't be Aa. Black horses are aa for Agouti, so it can be omitted in his genotype, as it doesn't influence his looks in any way.
Ee Aa would mean he's bay based.
He can be one of those - all those genotypes will result in same/similar looks:
- Ee Gg
- EE GG
- Ee GG
- EE Gg