10. Let $A$ and $B$ be two points on the parabola $y=x^{2}$ on opposite sides of the $y$-axis, distinct from $O$, such that $AB=4$. Denote the area of $\triangle AOB$ by $S$, where $O$ is the origin. Then the maximum value of $S$ is $\qquad$.
10.8.

Let $A\left(-m, m^{2}\right), B\left(n, n^{2}\right)(n, m>0)$. Then $16=(n+m)^{2}+\left(n^{2}-m^{2}\right)^{2} \geqslant(n+m)^{2}$.
Therefore, $m+n \leqslant 4$.
$$
\begin{array}{l}
\text { Hence } S=\frac{1}{2}\left(m^{2}+n^{2}\right)(m+n)-\left(\frac{1}{2} m m^{2}+\frac{1}{2} n n^{2}\right) \\
=\frac{1}{2}(m+n) m n \\
\leqslant \frac{1}{8}(m+n)^{3} \leqslant \frac{1}{8} \times 4^{3}=8,
\end{array}
$$

Equality holds if and only if $m=n=2$.