TeX source:
\begin{array}{rclll}\mathbb{D} &=& \mathbb{R} \cr\cr t\cdot e^{t-1}+e^t-e^{t-1} &=& 0 \\e^{t-1}\left(t+e^1-1\right) &=& 0 &\vert & :e^{t-1} \\t+e-1 &=& 0 &\vert& -e+1\\t &=& 1-e\approx -1{,}7183\end{array}