12. Given that $x_{1}$ is a root of the equation $x+\lg x=3$, and $x_{2}$ is a root of the equation $x+10^{x}=3$, the value of $x_{1}+x_{2}$ is $\qquad$ .
12. 3.

Point $A\left(x_{1}, \lg x_{1}\right)$ and point $B\left(x_{2}, 10^{x_{2}}\right)$ are symmetric with respect to the line $y=x$, so $x_{1}=10^{x_{2}}$, which means $x_{2}=\lg x_{1}$. Also, $x_{1}+\lg x_{1}=3$, hence $x_{1}+x_{2}=3$.