Question 985206
{{{z>0}}}
sign of {{{y}}} is uncertain.


{{{abs(x-y)=z}}}



CASE {{{x-y>=0}}}
{{{x-y=z}}}
{{{x=z+y}}}

trying {{{x=7}}}

{{{7=z+y}}}


CASE {{{x-y<0}}}
{{{-x+y=z}}}
{{{-x=z-y}}}
{{{x=y-z}}}

trying {{{x=-3}}}
{{{-3=y-z}}}

Use these results as a system of equations:
{{{7=z+y}}}...............eq.1
{{{-3=y-z}}}..............eq.2
-----------------------------------------add them
{{{7-3=cross(z)+y+y-cross(z)}}}

{{{4=2y}}}

{{{2=y}}}

and
{{{7=z+2}}}...............eq.1
{{{7-2=z}}}
{{{z=5}}}

so, your equation is: 

{{{abs(x-y)=z}}}

{{{abs(x-2)=5}}}


{{{drawing ( 600, 600, -10, 10, -10, 10,
circle(-3,5,.12),circle(7,5,.12),
graph( 600, 600, -10, 10, -10, 10, abs(x-2),5)) }}}