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Unable to solve a nonlinear set of equations with Solve

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Solve[E^(-\[Sigma]σ \[Tau]τ) k (1+T1 \[Sigma]+ T σ)^-n==Subscript[Mn == Subscript[M, 0] && 
  2*E^(-\[Sigma]σ \[Tau]τ) k (1+T1 \[Sigma]+ T σ)^(-1 - n) (n T+\[Tau]+TT \[Sigma]+ \[Tau]τ + T σ τ)==Subscript[M ==
    Subscript[M, 1]  && 
  1/2 E^(-\[Sigma]σ \[Tau]τ) k (1+T1 \[Sigma]+ T σ)^(-2 - n) (n T^2+n^2T^2 T^2+2+ n^2 T^2 + 2 n T \[Tau]+2τ + 
      2 n T^2 \[Sigma]σ \[Tau]+\[Tau]^2+2τ + τ^2 + 2 T \[Sigma]σ \[Tau]^2+T^2τ^2 \[Sigma]^2+ \[Tau]^2
      T^2 σ^2 τ^2)*6==Subscript[M*6 == Subscript[M, 2] && &&k
  k (-(1/6) E^(-\[Sigma]σ \[Tau]τ) n (1+n1 + n) (2+n2 + n) T^3 (1+T1 \[Sigma]+ T σ)^(-3 - n) - 
      1/2 E^(-\[Sigma]σ \[Tau]τ) n (1+n1 + n) T^2 (1+T1 \[Sigma]+ T σ)^(-2 - n) \[Tau]τ - 
      1/2 E^(-\[Sigma]σ \[Tau]τ) n T (1+T1 \[Sigma]+ T σ)^(-1 - n) \[Tau]^2τ^2 - 
      1/6 E^(-\[Sigma]σ \[Tau]τ) (1+T1 \[Sigma]+ T σ)^-n \[Tau]^3τ^3)==Subscript[M == Subscript[M, 3], {k, T, 
  n,\[Tau] τ}]   
Solve::incnst: Inconsistent or redundant transcendental equation. After reduction, the bad equation is 1-((1+T \[Sigma]σ)^n)^(1/n) == 0. >>
Solve::incnst: Inconsistent or redundant transcendental equation. After reduction, the bad equation is -1+((1+T \[Sigma]σ)^n)^(1/n) == 0. >>
Solve::incnst: Inconsistent or redundant transcendental equation. After reduction, the bad equation is 1-((1+T \[Sigma]σ)^(-1-n))^(1/(-1-n)) == 0. >>
General::stop: Further output of Solve::incnst will be suppressed during this calculation. >>
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]}]   
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. >>
Solve[E^(-σ τ) k (1 + T σ)^-n == Subscript[M, 0] && 
  2*E^(-σ τ) k (1 + T σ)^(-1 - n) (n T + τ + T σ τ) ==
    Subscript[M, 1] && 
  1/2 E^(-σ τ) k (1 + T σ)^(-2 - n) (n T^2 + n^2 T^2 + 2 n T τ + 
      2 n T^2 σ τ + τ^2 + 2 T σ τ^2 + 
      T^2 σ^2 τ^2)*6 == Subscript[M, 2] && 
  k (-(1/6) E^(-σ τ) n (1 + n) (2 + n) T^3 (1 + T σ)^(-3 - n) - 
      1/2 E^(-σ τ) n (1 + n) T^2 (1 + T σ)^(-2 - n) τ - 
      1/2 E^(-σ τ) n T (1 + T σ)^(-1 - n) τ^2 - 
      1/6 E^(-σ τ) (1 + T σ)^-n τ^3) == Subscript[M, 3], {k, T, 
  n, τ}]
Solve::incnst: Inconsistent or redundant transcendental equation. After reduction, the bad equation is 1-((1+T σ)^n)^(1/n) == 0. >>
Solve::incnst: Inconsistent or redundant transcendental equation. After reduction, the bad equation is -1+((1+T σ)^n)^(1/n) == 0. >>
Solve::incnst: Inconsistent or redundant transcendental equation. After reduction, the bad equation is 1-((1+T σ)^(-1-n))^(1/(-1-n)) == 0. >>
General::stop: Further output of Solve::incnst will be suppressed during this calculation. >>
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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 ?