Let x and y be the two numbers.
We have x+y=-11 (because their sum is -11)
⇒ x= -11-y.
On the other hand, we also have x*y= -24 (because their product is -24)
⇒ (-11-y)*y= -24
⇒ -y^2 -11y= -24
⇒ y^2+ 11y -24= 0
⇒ ...
⇒ y= (-11-sqrt(217))/2 or y= (-11+sqrt(217))/2
x= (-11+sqrt(217))/2 or x= (-11-sqrt(217))/2 .
Conclusion: the two numbers are (-11+sqrt(217))/2 and (-11-sqrt(217))/2~