A problem by GH Hardy

Algebra Level 2

$\frac 1{1},\ \frac {2}{1},\ \frac {1}{2},\ \frac {3}{1},\ \frac {2}{2},\ \frac {1}{3},\ \frac {4}{1},\ \frac {3}{2},\ \frac {2}{3},\ \frac {1}{4},\ \ldots$

If $\frac {1887}{1920}$ is the $m^\text{th}$ term and $\frac {1789}{2018}$ is the $n^\text{th}$ term of the sequence above, find $|m-n|.$

Note: In this sequence, the fractions do not reduce. For example, $\frac{2}{2}$ is distinct from $\frac{1}{1}.$