Basically, you have equation (x,y,z+x)=E(x,y,z) or (x,y,z)+(0,0,x)=E(x,y,z), which transforms into
(0,0,x)=(E-I)(x,y,z), where I is the unit matrix, I={(1,0,0);(0,1,0);(0,0,1)} Now denote E-I as U, then we have:
U_{11}x+U_{12}y+U_{13}z=0
U_{21}x+U_{22}y+U_{23}z=0
U_{31}x+U_{32}y+U_{33}z=x
Since x, y, and x are arbitrary, the only way to satisfy those three equations is to set all U_{ij} equal to zero, except U_{31}, which shall be set equal to 1. So U={(0,0,0};(0,0,0);(1,0,0)}
Then E can be easily found by adding U and I, E=U+I