13.321. The sum of two three-digit numbers, written with the same digits but in reverse order, is 1252. Find these numbers if the sum of the digits of each of them is 14, and the sum of the squares of the digits is 84.
Solution.

Let $100 x+10 y+z$ be the desired number. According to the condition, we have the system

$$
\left\{\begin{array}{l}
100 x+10 y+z+100 z+10 y+x=1252 \\
x+y+z=14 \\
x^{2}+y^{2}+z^{2}=84
\end{array}\right.
$$

from which $x=8, y=2, z=4$.

Answer: 824 and 428.