Another way is to find the perpendicular from center of the circle on to the line.
Line perpendicular to x-y+2 =0, is x+y=c
It passes through the center of the circle (-2,1)..
Hence, -2 + 1 = c => c = -1
Intersection of the two perpendicular lines y= x+2 and y = -x - 1 is
(-3/2 , 1/2)