For each integer $n \ge 100$ we define $T(n)$ to be the number obtained from $n$ by moving the two leading digits to the end. For example, $T(12345) = 34512$ and $T(100) = 10$. Find all integers $n \ge 100$ for which $n + T(n) = 10n$.
Problem
Source: 2021 Irish Mathematical Olympiad P3
Tags: number theory, Digits, decimal representation