Capital Gains on joint owned home with ex-spouse buying new home

I have been divorced for over 5 years. My ex-spouse and I have continued to co-own the house we bought in 1990 as our main residence. He has continued to live there, and I moved to a different state 5 years ago.  We are now selling that home and buying a new home, which will continue to be his main residence. I have no plan to live there, and he will be responsible for all upkeep and mortgage on the new home. 

My share of the profit on the sale of the original home would be $150,000 (50 % of the profit).  All of the profit will be used for the purchase of the new home. As I have not lived in the home recently, I am looking at the potential of a large capital gains tax. My income is less than $42000 / year. 

Is there some way I can avoid paying a large capital gains tax?  It was suggested I could sign a Quit Claim prior to the sale being finalized. Or to have a 1081 form used, but it was unclear whether it would work in this situation.  Thanks!