Let's use x and y for the two numbers and set up equations:
x*y = -1040
x + y = 14
x + y = 14
y = 14 - x
Let's substitute that into the first equation
x*(14 - x) = -1040.
14x - x^2 = -1040.
Move over everything to the write to get:
x^2 - 14x - 1040 = 0.
Now, let's use the quadratic formula to solve this:
http://www.math.com/students/calculators/source/quadratic.htm is a quick way to get the numbers.
We get x = 40 and x = -26
So, our two numbers are -26 and 40.