The operation $\nabla$ is defined by $g \nabla h=g^{2}-h^{2}$. For example, $2 \nabla 1=2^{2}-1^{2}=3$. If $g>0$ and $g \nabla 6=45$, the value of $g$ is
(A) 39
(B) 6
(C) 81
(D) 3
(E) 9
Using the definition of the operation, $g \nabla 6=45$ gives $g^{2}-6^{2}=45$.

Thus, $g^{2}=45+36=81$.

Since $g>0$, then $g=\sqrt{81}=9$.

ANswer: (E)