13.347. Find two numbers under the following conditions: their sum is 1244; if you append the digit 3 to the end of the notation of the first number, and remove the digit 2 from the end of the notation of the second number, two equal numbers will be obtained.
## Solution.

Let $x, y$ be the required numbers. According to the condition, we have the system $\left\{\begin{array}{l}x+y=1244, \\ 10 x+3=\frac{y-2}{10},\end{array}\right.$

from which $x=12, y=1232$.

Answer: 12 and 1232.