If $n$ is the largest positive integer with $n^{2}<2018$ and $m$ is the smallest positive integer with $2018<m^{2}$, what is $m^{2}-n^{2}$ ?
Since $\sqrt{2018} \approx 44.92$, the largest perfect square less than 2018 is $44^{2}=1936$ and the smallest perfect square greater than 2018 is $45^{2}=2025$.

Therefore, $m^{2}=2025$ and $n^{2}=1936$, which gives $m^{2}-n^{2}=2025-1936=89$.

ANSWER: 89