When do you use hyphen when writing numbers in words?

You use a hyphen only when 2 numbers are combined to make a single number.

In your example, the only 2 numbers which are combined are 'eighty' and 'two', or '82'. Writing it out in full would be (note the commas and the 'and'):

Seventy thousand, six hundred and eighty-two.

Here's another number: 24,976,155

There are 3 'combined' numbers: 24, 76, and 55:

Twenty-four million, nine hundred and seventy-six thousand, one hundred and fifty-five.

Writing Numbers Hyphen