Finding all integers $m$ and $n$ satisfying $\frac{1}{m}-\frac{1}{n}=\frac{1}{100}$

Question

So my older brother posed this question to me and I've been stuck on it for a long time.

Find all integers $m$ and $n$ that satisfy $$\frac{1}{m}-\frac{1}{n}=\frac{1}{100}$$

(He actually said a $2$ digit multiple of $3$ instead of $100$ but...yea.)

So this is what I have so far:

1. multiply both sides by $mn100:$ so then $100n-100m=mn$
2. try to factor $n(100-m)-100m=0.$ And that is where I'm stuck. I know $SFFT$ (Simon's Favorite Factoring Trick) but it doesn't seem to work here no matter what I subtract.

Can I please have a hint as to what to add or subtract? Thank you!