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    $\begingroup$ NSolve works when restricted to reals: NSolve[x==Cos[x],x,Reals] gives {{x -> 0.739085}}. $\endgroup$ Commented Oct 22, 2012 at 6:58
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    $\begingroup$ The "Dottie number" is not known to have an explicit closed form. $\endgroup$ Commented Oct 22, 2012 at 7:12
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    $\begingroup$ Strongly related: Can Reduce really not solve for x here? $\endgroup$ Commented Oct 22, 2012 at 11:25