58th Ukrainian National Mathematical Olympiad

Let $abcd$ denote the number Andriy wrote, then $\overline{abcd}-\overline{abc}=2018$. Now we only need to pick corresponding digits. Obviously, $a=2$ or $a=3$.

With $a=3$, $\overline{3bcd}-\overline{3bc}>3000-399>2018$, hence, $a=2$ and $\overline{2bcd}-\overline{2bc}=2018$. Analogously, $b=2$ or $b=3$.

With $b=3$, $\overline{33cd}-\overline{33c}>3300-339>2018$, therefore, $b=2$ and $\overline{22cd}-\overline{22c}=2018$. Analogously, $c=3$ or $c=4$.

When $c=4$, we get $\overline{224d}-\overline{224}>2240-224=2016$, therefore, the first solution would be in the form: $2242-224=2018$.

When $c=3$, we get $\overline{223d}-\overline{223}<2239-223=2016$, which means previously found solution is unique possible.