Is there a viewer I can use to open my IndividualTaxReturn.TAX2010 file and my IndividualTaxReturn.TAX2011 file?

No.  The IRS does not save tax returns for more than seven years, nor does TurboTax.

Why do you need to review those forms ?

You could try the TaxPrinter service at  http://www.taxprinter.com

They might be expensive and it is probably not safe to email tax returns back and forth  Their Website says…….

We read most federal and state files (Windows and Macintosh) from years 1996, 1997, 1998, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 and 2017. Known exceptions are TurboTax 1997, 1999 and TaxCut 2005 files which we can't read for technical reasons. TurboTax 1998 and 2002 files may show only the tax summary and the Form 1040.

did you check ebay? not sure whether you would be able to obtain the updates.....

some websites sell old TT software.  don't buy. they are beta versions, not updateable, and will not reflect the actual laws in effect for those years, opening your tax files with old, out of date software will change the files.