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

    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}]

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 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. >>

This system can be solved.

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