Problem 5. The sum of two natural numbers is 2018. If the digit in the units place of one is crossed out, the other number will be obtained. Find all such numbers.
Solution. Let the numbers be $x$ and $y$ and let $x>y$. Then $x=10 y+k$, where $k$ is the crossed-out digit. Now we have $x+y=10 y+k+y=11 y+k$, so $11 y+k=2018$. Therefore, $k$ is the remainder of the division of 2018 by 11, i.e., $k=5$. According to this, $11 y+5=2018$, so $y=183$. It follows that $x=1835$.