I have both VS2005 and VS2008 installed on my machine. I was able to install Team Explorer 2008, but could not install Team Explorer 2005 (it kept throwing some error number 2337 which I could not resolve).
Currently, I am having to launch the VS2008 IDE for using source control, and VS2005 for working on the source code (as the projects and solution files are still in the older VS2005 format).
Can I TE2008 to work with VS2005 in order to have an integrated experience?
You must have the the 2005 version of Team Explorer installed for the TFS integration to be present in VS 2005. Visual Studio 2005 + Team Explorer 2005 can happily co-exist on a machine with Visual Studio 2008 + Team Explorer 2008 and run side by side.
So, to get this to work you need to work past your 2337 error. The only times when I have seen that error myself have been where the Team Explorer installer was corrupted. You could try re-downloading it or accessing it from a Team Foundation Server 2005 installation CD.
Hope that helps,
Martin.