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

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

$\displaystyle n=0,1,2....$

$\displaystyle m<\infty$

where

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

$\displaystyle k_{n}$ are constants

or is it even possible to solve such a system ?