The interactions between planar brushes of adsorbed telechelic polymers are investigated via a self-consistent mean-field calculation via the strong stretching approximation. By allowing the relaxation of the loops upon the initiation of bridging, we obtain a stronger attraction than from Milner and Witten's analysis that excludes this effect. The entropy of ends is the origin of the attraction, but excluded-volume interactions play a role. The interaction potential in kT per chain is determined by the dimensionless separation and a single dimensionless parameter, the extent of stretching normalized by the size of a Gaussian coil.