10. The equation $x^{2}+a|x|+a^{2}-3=0$ $(a \in \mathbf{R})$ has a unique real solution. Then $a=$
10. $\sqrt{3}$.

Since $f(x)=x^{2}+a|x|+a^{2}-3$ is an even function, the only real solution must be 0, so $a^{2}-3=0$ and $a>0$. Therefore, $a=\sqrt{3}$.