See publication 523 on page 6.
https://www.irs.gov/pub/irs-pdf/p523.pdf
The IRS publishes several "safe harbor" rules -- if you meet these circumstances, they will assume you qualify for a partial exclusion. You don't meet the safe harbor because your commute from your old house to your new job is not 50 miles longer than your commute from your old house to your old job. However, you may still be able to claim a partial exclusion if you can show by your unique facts and circumstances that keeping the old house was financially or in some other way unreasonable. Don't send proof with your tax return, but keep it with your important tax papers for at least 3 years in case of audit.
