Are you looking for solutions to that equation?

Solve[Exp[x] == Cos[x] && -10 <= x <= 10, x, Reals]

(* Out[90]= {{x -> 0}, {x -> 
   Root[{-E^#1 + Cos[#1] &, -7.8535932799712482001}]}, {x -> 
   Root[{-E^#1 + Cos[#1] &, -4.7212927588476862166}]}, {x -> 
   Root[{-E^#1 + Cos[#1] &, -1.29269571937339838117}]}} *)

Or an iterative process that finds a solution from a starting point. For that one can use e.g. Newton iterations.

FixedPointList[{#[[1]] - f[#[[1]]]/f'[#[[1]]], 
   f[#[[1]]]} &, {-.7, f[-.2]}]

(* Out[112]= {{-0.7, -0.1613358247632598}, {-2.51705989723243, \
-0.268256883493079}, {-0.7474281702634069, 
  0.8919329283107287}, {-2.007816769456799, -0.2598565433504163}, \
{-1.285388510652165, 
  0.5575233413007432}, {-1.292717416706861, -0.005005670608255908}, \
{-1.2926957195615, 0.00001490725795189052}, {-1.292695719373398, 
  1.292351226034327*10^-10}, {-1.292695719373398, \
-5.551115123125783*10^-17}, {-1.292695719373398, \
-5.551115123125783*10^-17}} *)

I get an empty plot in Mathemaca 10 running under Linux.

Thanks, Daniel, for pointing out this site to me.

It seems, however, that in contrast to StackExchangeMMA Latex is not supported here. Example:

$\sqrt{1+x^2}$

Or am I doing something wrong?

I have gradually become acustomed to using it for better readability in texts.

Regards, Wolfgang