Let one of the numbers be x and the other is y.

Given that the sum of the numbers is 12.

==> x + y= 12............(1)

Also, given that the product is 27.

==> x*y = 27...............(2)

Then we have a system of two equations ans two variables.

We will use the substitution method to solve.

From (1) we know that x= 12-y

==> x*y = 27

==> (12-y)*y = 27

==> 12y - y^2 = 27

==> y^2 - 12y + 27 = 0

Now we will factor.

==> (y-9)(y-3) = 0

==> y1- 9 ==> x1= 12-9 = 3

==> y2= 3 ==> x2 =12-3 = 9

**Then the numbers are 3 and 9.**

Let the numbers we have to find be A and B

As the sum of the numbers is 12

=> A + B = 12

=> A = 12 - B

Their product is 27

=> AB = 27

Substituting A = 12 - B

=> (12 - B)*B = 27

=> 12B - B^2 = 27

=> B^2 - 12B + 27 = 0

=> B^2 - 9B - 3B + 27 = 0

=> B(B - 9) - 3(B - 9) = 0

=> (B - 3 )(B - 9) = 0

B = 3 or 9

A = 9 or 3

**The required numbers are 3 and 9.**