is there something like word math, where you can add or subtract words to make new words? maybe even multiply or divide words too?

You can subtract words too.

I think yes. For example, you can add -ing to sing. But you can't multiply or divide words.

if you used a base 36 numbering system it would be possible, since all letters would then represent a numerical value

Do you mean a base 26?

It would not have to be base 26, you could do this just with base 10 but the numbers for the letters would be 1 to 26 or 0 to 25.  Maybe a hyphen could have a 27th value?