I'm not sure this is what you are looking for. If it isn't then try to explain what I've misunderstood and I'll try again.

First satisfy Mathematica's capitalization and [] versus() requirements and then combine the left and right sides of your equality and plot the result to see where to start looking for the desired x, experiment with plot range until you find an informative plot. But tuck away for the future that Plot isn't necessarily perfect and for really really nasty equations Plot can sometimes give you misleading results or even just a blank page.

In[1]:= Plot[-3 + 4 Log[x] + E^x - x^2, {x, 0, 6}]

Out[1]= ...PlotSnipped...

Then use that information about where the root might lie to help guide FindRoot.

In[2]:= FindRoot[-3+4 Log[x]+E^x-x^2,{x,1.5}]

Out[2]= {x->1.29307}

It is even possible, if you look at the help page for FindRoot and know enough to click on "Details and Options", to discover that you can tell FindRoot the variable to use, the initial value and the upper and lower limits to restrict the search range. That is particularly helpful when you are pretty sure you know where the root should be, but you equation is complicated enough that otherwise FindRoot will get lost wandering further and further away from the root you actually desire. (Bumping that information on how FindRoot up can be used with start, min and max above the "Details and Options" line seems like it would be very helpful because again and again I see new users missing this completely and I didn't realize to look there for long enough that I'm embarrassed.)

The FindRoot method with appropriate information to limit the search, is usually far more successful than trying to use Solve or Reduce with complicated problems.

And if this isn't enough then provide a few more hints, or even everything, about your nasty equation and perhaps someone can find another way to get the solution.