You can translate the two statements from English to math:
#stackrel(x+y) overbrace"The sum of two numbers"" " stackrel(=) overbrace"is"" " stackrel(-28) overbrace"-28."#
#stackrel(x*y) overbrace"The product of the same two numbers"" " stackrel(=) overbrace"is"" " stackrel(96) overbrace"96."#
Now we can create a system of equations:
#{(x+y=-28, qquad(1)), (x*y=96, qquad(2)):}#
Now, solve for #x# in equation #(1)#:
#color(white)(=>)x+y=-28#
#=>x=-28-y#
Plug this new #x# value into equation #(2)#:
#color(white)(=>)x*y=96#
#=>(-28-y)*y=96#
#color(white)(=>)-28y-y^2=96#
#color(white)(=>)-y^2-28y-96=0#
#color(white)(=>)y^2+28y+96=0#
#color(white)(=>)(y+24)(y+4)=0#
#color(white)(=>)y=-4,-24#
Lastly, plug both of these #y# values back into equation #(1)#:
For #y=-4#:
#color(white)(=>)x+y=-28#
#=>x-4=-28#
#color(white)(=>)x=-24#
And for #y=-24#:
#=>x-24=-28#
#color(white)(=>)x=-4#
Finally, we see that there are two solutions which are the same: #(-4,-24)# and #(-24,-4)#.
This means that the two numbers are #-4# and #-24#.
