what two number have the product of 144 and the sum of 30

Let x be the first number and y  be the second

So

x + y = 30       and   xy = 144

So,  using the first equation, y = 30 - x      and substituting into the second, we have

x(30 - x) = 144

30x - x² = 144    and rearranging, we have

x² - 30x + 144 = 0   and factoring, we have

(x - 6) (x - 24) = 0 and setting each factor to 0, we have  ...    x = 6  and y = 24      or   x = 24  and y = 6