When the square of one number is subtracted from the square of another number, the difference is 1 less than the square of 9. find the missing numbers.

There's not enough information given to find a definite solution for the two numbers. Instead there will be many solutions. Two variable problems require either a second equation, a value for one of the variables or a relation given between them. (like if they're consecutive integers or one is twice the other)

So, what you can do is write out the equation and "guess and test" till you find two integers that work.

x^2 - y^2 = 9^2 - 1

x^2 - y^2 = 80

y = sqrt( x^2 - 80)

putting in integer values for x starting at 9.

1 = sqrt(81 - 80)
(9, 1) works likewise so would (-9,1) (-9,-1) as well as (12, 8)