Subscript[E, 1] = (x^2 Exp[x])/(Exp[x] - 1)^2; infl = Reduce[\!\( \*SubscriptBox[\(\[PartialD]\), \({x, 2}\)] \*SubscriptBox[\(E\), \(1\)]\) == 0, x, Reals]
Plot[Subscript[E, 1], {x, -5, 5}, Epilog -> {Red, PointSize[0.025], Point[{x, Subscript[E, 1]}] /. {ToRules[infl]}}]