UKMT Junior Mathematical Olympiad, 2026

In the following sum, the letters $Y$, $U$, $M$ and $S$ stand for single digits.
$$\begin{array}{r} Y\,U\,M\,S \\ +\,\,\,Y\,U\,M \\ \hline 2\,0\,2\,6 \end{array}$$
Prove that this is the only possible solution. A full explanation is required.