Missing Number

Fix $n \geq 2$. A subset $S \subseteq [n] = \{1,2,\dots, n\}$ of size $n-2$ is selected. You are given that $\displaystyle \sum_{s \in S} s = s_1$ and $\displaystyle \sum_{s \in S} s^2 = s_2$. If possible, find the two missing values when $n = 50, s_1 = 1231,$ and $s_2 = 41619$. Report the concatenation of the two numbers, with smaller number first. For example, if the two missing numbers were $12$ and $34$, report $1234$ as the answer.