8.2 Let $s(n)$ denote the sum of the digits of a natural number $n$. Solve the equation $n+s(n)=2018$.
Answer: $n=2008$. Solution. Since $n2018-29=1989$, i.e., $n$ is written in the form $\overline{199 x}$ or $\overline{200 x}$ or $\overline{201 x}$ where $x$ is some digit. In the first case, we have the equation $1990+x+19+x=2018$, which gives a non-integer value of $x$. Similarly, in the third case, the equation $2010+2 x+3=2018$ gives a non-integer $x$. In the second case, the equation $2000+2 x+2=2018$ gives $x=8$, i.e., $n=2008$.