Example 2. Rearrange the digits of a three-digit number to form the largest possible three-digit number, and subtract the smallest digit from it, which is exactly equal to the original number. Find these three digits. (Hua Luo Geng Math Contest 1988 Junior High School Level)
Let the three-digit number be $a, b, c$. If $abc$ is the largest, and $cb_{2}$ is the smallest, and
$$
\begin{array}{l}
\overline{a b c}-cba \\
=\left(10^{2} a+10 b+c\right)-\left(10^{2} \cdot c+10 b+a\right) \\
=99(a-c),
\end{array}
$$

i.e., the required three-digit number is a multiple of 99. Among such three-digit numbers $198, 297, 396, 495, 594, 693, 792, 891$, only 495 meets the condition. Therefore, the required three-digit number is 495.

This problem uses the fact that the difference between a three-digit integer and its reverse is a multiple of 99. If this result is not used, various cases need to be discussed separately, making the solution process quite cumbersome.