How many ordered integer pairs $(x,y)$ ($0\leq x,y < 31$) are there satisfying $(x^2-18)^2\equiv y^2 (\mod 31)$?

$ \textbf{(A)}\ 59
\qquad\textbf{(B)}\ 60
\qquad\textbf{(C)}\ 61
\qquad\textbf{(D)}\ 62
\qquad\textbf{(E)}\ \text{None}
$