The line T1+ 2T2= 14 is a diagonal of the rectangle with vertices (1,2), (10, 4), (10,6), and (1,6). The joint p.d.f is a constant, 1 over area of the triangle with vertices (1,2), (10,4), and (1,6).

Graph that region and the line T1+ T2= 10. That will cut the region above in two points, where T1+ T2= 10 intersects T1+ 2T2= 15, and where T1+ T2= 10 intersects T2= 2. P(T1+T2> 10) is the constant above multiplied by the area of the triangle with those two points and (10, 2) as vertices.