smc

Each of the graphs consists of two orthogonal half-lines. In the first graph both point downwards at a $45^{\circ }$ angle, in the second graph they point upwards. One can easily find out that the only way how to get these graphs to intersect in two points is the one depicted below: Obviously, the maximum of the first graph is achieved when $x=a$, and its value is $-0+b=b$. Similarly, the minimum of the other graph is $(c,d)$. Therefore the two remaining vertices of the area between the graphs are $(a,b)$ and $(c,d)$. As the area has four right angles, it is a rectangle. Without actually computing $a$ and $c$ we can therefore conclude that $a+c=2+8=\boxed{10}$.