Question 551147
Let the 10's digit = {{{a}}}
Let the 1's digit = {{{ b }}}
given:
(1) {{{ a + b = 8 }}}
(2) {{{ ( 10b + a ) - ( 10a + b ) = -18 }}}
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(2) {{{ 10b + a - 10a - b = -18 }}}
(2) {{{ -9a + 9b = -18 }}}
Multiply both sides of (1) by {{{9}}}
and add (1) and (2)
(1) {{{ 9a + 9b = 72 }}}
(2) {{{ -9a + 9b = -18 }}}
{{{ 18b = 54 }}}
{{{ b = 3 }}}
and, since
(1) {{{ a + b = 8 }}}
(1) {{{ a + 3 = 8 }}}
(1) {{{ a = 5 }}}
The original number is 53 
check answer:
(2) {{{ ( 10*3 + 5 ) - ( 10*5 + 3 ) = -18 }}}
(2) {{{ 30 + 5 - 50 - 3 = -18 }}}
(2) {{{ 35 - 53 - -18 }}}
(2) {{{ -18 = -18 }}}
OK