CN-TST 2017 Problem 23

Given integer $m\geq2$ , $x_1,...,x_m$ are non-negative real numbers,prove that: $$(m-1)^{m-1}(x_1^m+...+x_m^m)\geq(x_1+...+x_m)^m-m^mx_1...x_m$$ and please find out when the equality holds.