No. 2010? Is that a typo? TurboTax and the IRS only save tax returns for seven years. After seven years they are gone.
Doubtful that you can get a copy from your employer for tax year 2010. Nor a wage and income transcript or a copy of the 2010 return from the IRS, but you can try.
If you cannot obtain the W-2 from your employer, then for a fee you can get a complete copy of a W-2 from the Social Security Administration - https://faq.ssa.gov/en-us/Topic/article/KA-02501
You can get a free Wage and Income transcript from the IRS - https://www.irs.gov/individuals/get-transcript
For a fee of $43 you can get a complete federal tax return to include copies of W-2's, if you mailed the tax return and included a paper W-2, from the IRS by completing Form 4506 - http://www.irs.gov/pub/irs-pdf/f4506.pdf
See this IRS Tax Topic - http://www.irs.gov/taxtopics/tc159.html
if you really want your 2010 w-2 (not your tax return), the only source is the Social Security Adm
https://faq.ssa.gov/en-us/Topic/article/KA-02501