The only way to open a .tax2010 tax return file is with the TurboTax software for 2010. The 2010 software is no longer available, so you would only be able to use it if you already have it installed. 

If you used TurboTax Online, you may be able to access your 2010 income tax return. See How do I access a prior year return?

I have the 2010 version installed, however, I get an error message that says it cannot open the 2010 file because it was completed with an older version of TurboTax. It is labeled 2010.

there are certain web services that for a fee can take your .tax2010 file and print out a return. the risk is yours because you would have to send them the file which has all your personal information. if the .tax2010 file is corrupt there may be no way to recover the return.  the IRS only keeps returns for 7 years so they would not have a copy any longer.