$2.15 \sqrt{x^{2}+9}-\sqrt{x^{2}-7}=2$.
### 2.15 We have

$$
\begin{aligned}
& \left(x^{2}+9\right)-\left(x^{2}-7\right)=16, \text { or } \\
& \left(\sqrt{x^{2}+9}-\sqrt{x^{2}-7}\right)\left(\sqrt{x^{2}+9}+\sqrt{x^{2}-7}\right)=16
\end{aligned}
$$

Since $\sqrt{x^{2}+9}-\sqrt{x^{2}-7}=2$, then $\sqrt{x^{2}+9}+\sqrt{x^{2}-7}=8$.

Therefore, we obtain the system

$$
\begin{aligned}
& \left\{\begin{array}{l}
\sqrt{x^{2}+9}+\sqrt{x^{2}-7}=8 \\
\sqrt{x^{2}+9}-\sqrt{x^{2}-7}=2
\end{array}\right. \\
& \text { from which } 2 \sqrt{x^{2}+9}=10, \text { i.e., } x_{1,2}= \pm 4
\end{aligned}
$$

Solution: $x_{1,2}= \pm 4$.