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Can Reduce *really* not solve for x here?

Why can't Mathematica solve this equation?

f[x_] := Exp[Cos[3*x]]
g[x_] := (1/3)*x^3 - x^2 + 2
Solve[f[x] == g[x], x]
(* Solve::nsmet: This system cannot be solved with the methods available to Solve. >> *)
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    $\begingroup$ Use e.g. Solve[f[x] == g[x] && Abs[x] < 10, x, Reals]. For more detailed discussion of transcendental equations see e.g. mathematica.stackexchange.com/questions/4694/…, a general issue of Root see e.g. mathematica.stackexchange.com/questions/13767/… $\endgroup$
    – Artes
    Commented Dec 15, 2012 at 21:17
  • $\begingroup$ You can still solve this equation without assuming x to be real, but then the system might be unable to prove that there were all solutions found. Assuming Reals one gets 5 solutions, while assuming Complex one gets 385 solutions. $\endgroup$
    – Artes
    Commented Dec 15, 2012 at 21:23
  • $\begingroup$ thanks a lot! you saved my life right there :) $\endgroup$
    – MKh
    Commented Dec 16, 2012 at 15:30

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