how to solve a nonlinear system of algebraic equations of this form :

\sum^{m}_{i=1}x^{n}_{i}=k_{n}

n=0,1,2....

m<\infty

where

\sum^{m}_{i=1}x^{n}_{i} is a power sum polynomial

k_{n} are constants

or is it even possible to solve such a system ?