Question 501144
Call the 1st number {{{a}}}
Call the 2nd number {{{b}}}
given:
(1) {{{ a + b = 2a - 8 }}} ( The sum of two numbers is 8 less than twice the first number )
(2) {{{ a - b = 2b - 4 }}} ( Their difference is 4 less than twice the second number )
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Two or more equations is called a "system" of equations.
In order to solve, the number of equations has to equal 
the number of unknowns. You have 2 equations and
2 unknowns, so it's solvable.
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(1) {{{ a + b = 2a - 8 }}}
Subtract {{{ 2a }}} from both sides
(1) {{{ b - a = -8 }}}
and
(2) {{{ a - b = 2b - 4 }}}
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Adding (1) and (2),
{{{ 0 = -8 + 2b - 4 }}}
Add {{{ 12 }}} to both sides
{{{ 2b = 8 + 4 }}}
{{{ 2b = 12 }}}
{{{ b = 6 }}}
and, since,
{{{ b - a = -8 }}}
{{{ 6 - a = -8 }}}
Add {{{8}}} to both sides
{{{ 14 - a = 0 }}}
Add {{{a}}} to both sides
{{{ a = 14 }}}
The numbers are 14 and 6
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Note that for equation (2), if I had said
(2) {{{ b - a = 2b - 4 }}}, I end up with negative answers,
so I avoided that.