Question

What two numbers multiply to 16 and add to 4?

Answer 1

You said that (xy) = 16, and (x+y) = 4 .

From the second equation you can get [ x = 4 - y ],
then substitude that for 'x' in the first equation, and
finally, rearrange the first equation to read
                                                                   x² - 4x + 16 = 0

Don't even try to factor that quadratic equation.  Go straight
to the quadratic formula, and the two solutions you find are ...

         x = 2 + i 2√3
and
         x = 2 - i 2√3 .

Those are the two number that do what you want.

There are no real numbers that can do it.

Answer 2

Xy=16               
 x + y = 4
-----------------

Solve those two equations for x and y.

The two numbers are:  2 - 2i sqr(3) and  2 + 2i sqr(3)