Technically the TE may not require .NET Framework, but for some reason when HTC was preparing the TE for deployment, they did not incorporate the required policy (policy_9_0_microsoft_vc90_crt _x86.msm) to install the dependent Mirosoft.VC90.CRT files. (At least that is what I’m guessing.)
I was getting the same "application has failed to start" error and updating .Net Framework to Service Pack 1 moved me from VC80 to VC90 which was needed to run the TE. There may be other ways then updating .NET Framework to get the required dependent assemblies that where not included with the TE.