7.085. $10^{1+x^{2}}-10^{1-x^{2}}=99$.
Solution.

We have $10 \cdot 10^{x^{2}}-\frac{10}{10^{x^{2}}}-99=0 \Rightarrow 10 \cdot 10^{2 x^{2}}-99 \cdot 10^{x^{2}}-10=0$. Solving this equation as a quadratic in terms of $10^{x^{2}}$, we get $10^{x^{2}}=-\frac{1}{10}, \varnothing$, or $10^{x^{2}}=10$, from which $x^{2}=1, x_{1,2}= \pm 1$.

Answer: $-1 ; 1$.