10. Given $P_{0}(1, f(1))$ is a point on the curve $C: f(x)=\mathrm{e}^{x}$, the tangent line $l_{1}$ of $C$ at $P_{0}$ intersects the $x$-axis at point $Q_{1}\left(x_{1}, 0\right)$, a vertical line through $Q_{1}$ intersects $C$ at $P_{1}$, the tangent line $l_{2}$ of $C$ at $P_{1}$ intersects the $x$-axis at $Q_{2}\left(x_{2}, 0\right)$, a vertical line through $Q_{2}$ intersects $C$ at $P_{2}$, the tangent line $l_{3}$ of $C$ at $P_{2}$ intersects the $x$-axis at $Q_{3}\left(x_{3}, 0\right)$, a vertical line through $Q_{3}$ intersects $C$ at $P_{3}$, and so on, find $x_{2023}$.
The equation of the tangent line to $f(x)$ at $P_{n}\left(x_{n}, f\left(x_{n}\right)\right)$ is $y-\mathrm{e}^{x_{n}}=\mathrm{e}^{x_{n}}\left(x-x_{n}\right)$. Let $y=0 \Rightarrow x_{n+1}=x_{n}-1$. Combining $x_{0}=1 \Rightarrow x_{1}=0 \Rightarrow x_{n}=-n+1$. Therefore, $x_{2023}=-2022$.