How would you solve in algebraic terms the value of two numbers when one number is greater than the other number by 9 and their product is 322?

Let one number be x+9 and the other x:-

(x+9)*x = 322

x2+9x-322 = 0

Solving the above by means of the quadratic equation formula gives x a positive value of 14.

So the numbers are 14 and 14+9 = 23

Check: 14*23 = 322