Case 1: If (x-2)>=0, equation will be reduced to
$(x-2)^{2} + (x-2) - 2 =0$
i.e. x=0,3
x=0 will not be accepted as (x-2) will be less than 0
Case 2: If (x-2)<0, equation will be reduced to
$(-(x-2))^{2} - (x-2) - 2 =0$
i.e. x=1,4
x=4 will not be accepted as (x-2) will be greater than 0
Sum of all real roots = 3+1=4