China Mathematical Competition

It is easy to find that $B\subseteq \{-2,0,-1,-3\}$. We have $2-x^2\notin A$ when $x=-2,-3$, and $2-x^2\in A$ when $x=0,-1$. Therefore, $B=\{-2,-3\}$, the sum of whose elements is $-5$. The answer is $-5$.