Super Key is any set of attributes that uniquely determines a tuple in a relation.
Since $E$ is the only key, $E$ should be present in any super key.
Excluding $E$, there are three attributes in the relation, namely $F, G , H$. Hence, if we add $E$ to any subset of those three attributes, then the resulting set is a super key. Number of subsets of $\{F, G, H\}$ is $8$. Hence the answer is $8$.
The following are Super Keys: $$\left \{ \substack{E\\EF\\EG\\EH\\EFG\\EFH\\EGH\\EFGH} \right \}$$