If you open this file and scroll to the bottom, you will likely notice errors (which are highlighted in red). The error messages I was getting were:
SetSite failed for package [Microsoft.VisualStudio.TeamFoundation.VersionControl.HatPackage, Microsoft.VisualStudio.TeamFoundation.VersionControl, Version=11.0.0.0, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a]
End package load [Microsoft.VisualStudio.TeamFoundation.VersionControl.HatPackage, Microsoft.VisualStudio.TeamFoundation.VersionControl, Version=11.0.0.0, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a]This was traced back to a config file located at: "C:\Users\USERNAME\AppData\Local\Microsoft\Team Foundation\4.0\Cache\VersionControl.config" which needed to be deleted.\
After deleting the config file, open up Visual Studio and Team Explorer should now work as expected.