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Unable to solve a nonlinear set of equations with Solve

I'm trying to solve the following equation using Mathematica 9.0.1.0 :

Solve[E^(-\[Sigma] \[Tau]) k (1+T \[Sigma])^-n==Subscript[M, 0] && 2*E^(-\[Sigma] \[Tau]) k (1+T \[Sigma])^(-1-n) (n T+\[Tau]+T \[Sigma] \[Tau])==Subscript[M, 1]  && 1/2 E^(-\[Sigma] \[Tau]) k (1+T \[Sigma])^(-2-n) (n T^2+n^2 T^2+2 n T \[Tau]+2 n T^2 \[Sigma] \[Tau]+\[Tau]^2+2 T \[Sigma] \[Tau]^2+T^2 \[Sigma]^2 \[Tau]^2)*6==Subscript[M, 2]  &&k (-(1/6) E^(-\[Sigma] \[Tau]) n (1+n) (2+n) T^3 (1+T \[Sigma])^(-3-n)-1/2 E^(-\[Sigma] \[Tau]) n (1+n) T^2 (1+T \[Sigma])^(-2-n) \[Tau]-1/2 E^(-\[Sigma] \[Tau]) n T (1+T \[Sigma])^(-1-n) \[Tau]^2-1/6 E^(-\[Sigma] \[Tau]) (1+T \[Sigma])^-n \[Tau]^3)==Subscript[M, 3],{k,T,n,\[Tau]}]   

Mathematica outputs the following error:

Solve::nsmet: This system cannot be solved with the methods available to Solve. >>

And when I try to use "SolveAlwyas" instead of "Solve" I get the following errors :

Solve::incnst: Inconsistent or redundant transcendental equation. After reduction, the bad equation is 1-((1+T \[Sigma])^n)^(1/n) == 0. >>
Solve::incnst: Inconsistent or redundant transcendental equation. After reduction, the bad equation is -1+((1+T \[Sigma])^n)^(1/n) == 0. >>
Solve::incnst: Inconsistent or redundant transcendental equation. After reduction, the bad equation is 1-((1+T \[Sigma])^(-1-n))^(1/(-1-n)) == 0. >>
General::stop: Further output of Solve::incnst will be suppressed during this calculation. >>

This system can be solved.

Is there any way to solve this equations with Mathematica without giving numerical values to the parameters ?