Solution: Because these two circles intersect at the point (1, 3) (m,-1), the straight line connecting the centers of the two circles is the same as the straight line of the two intersections.

These lines are perpendicular to each other. The midpoint of a straight line connecting two intersections is on a straight line connecting the centers of two circles.

Because the centers of two circles are on the straight lines x-y+c=0 and k= 1, K 1=- 1.

According to the slope formula (-1-3)/(m-1) =-1.

So m=5

The midpoint coordinates of a straight line connecting two intersections are [( 1+m)/2, 1] = (3, 1).

So bring the point (3, 1) into the straight line x-y+c=0.

So m+c=3.