On a functional equation arising from comparison of utility representations

We solve the functional equation F1(t)−F1(t+s)=F2[F3(t)+F4(s)] for real functions defined on intervals, assuming that F2 is positive valued and strictly monotonic and that F3 is continuous. The equation arose from the equivalence problem of utility representations under assumptions of separability, homogeneity and segregation (e-distributivity).