Question 73655
Let the two numbers be a and b.  From the problem description, you can write:
1) {{{a+b = 12}}}  and
2) {{{a^2-b^2 = 48}}}
Rewrite equation 1) as: a = 12-b and substitute for the a in equation 2).
2a) {{{(12-b)^2-b^2 = 48}}} Simplify and solve for b.
{{{(144-24b+b^2)-b^2 = 48}}}
{{{144-24b = 48}}} Add 24b to both sides.
{{{144 = 48+24b}}} Subtract 48 from both sides.
{{{96 = 24b}}} Divide both sides by 24.
{{{4 = b}}} and...
{{{a = 12-b}}}
{{{a = 12-4}}}
{{{a = 8}}}
The two numbers are 4 and 8
Check:
{{{a+b = 8+4}}} = 12 Their sum is 12.
{{{a^2-b^2 = 8^2-4^2}}}
{{{64-16 = 48}}} The difference of their squares is 48.