Question 722560
Solution:

Let 'a' and 'b' are the 2 numbers.
Given : a * b = -240             --------eq.1
        a + b = 34 or b = 34 - a --------eq.2

Put 2 in 1, we get

a (34 - a ) = -240

34a - a^2 + 240 = 0

{{{a^2 - 34 a - 240 = 0 }}}
Solving the quadratic equation
{{{a^2 - 40a + 6a - 240 = 0}}}
{{{ a(a-40) +6(a + 40) = 0}}}
{{{(a-40)(a+6)=0}}}

a = 40 or a = -6

b = -6  or 40