Getting divorced without a separation agreement was not a good idea. This all should have been handled in your divorce in equitable distribution or via a marital settlement/separation agreement.
However, what is done is done. I assume that your name is still on the deed and that the property is in NC. Your options are: (1) make an offer to buy out your ex-wife's share of the equity in the home; (2) bring a partition action. If the property cannot be divided in partition then it will be sold. Unless there is some kind of restriction, then anyone can bid at the sale, but if you bid how is this different from buying out your ex-wife? With a partition sale, there is always a chance that you will be outbid. If you buy out your wife for the fair market value of the net equity, you will not have to worry about this. (3) file bankruptcy if you can file a chapter 7. This will discharge your liability on the mortgage. If your ex-wife wants it, she is going to have to pay for it or the bank will foreclose. Of course, the bankruptcy will be on your credit but if the house is worth less than what is owed, this may be a viable option. (4) Stop paying on the mortgage. The bank will foreclose. Again, this will be on your record. This may also be an option if the value of the house is less than what is owed or about equal to it. You will run the risk of the bank coming after you for a deficiency but you could always hold off and see if they do. If not, then you will not have to worry about this and your credit will eventually recover. (5) The smartest and best thing you could do is if your ex-wife is agreeable, you could put the house up for sale. But this would require you and your ex-wife to get the house ready for showing, get her to move out and for you both to agree on the realtor, selling price.
There is no other way to get fair market value that I am aware of. Partition and foreclosure sales are fire-sales and bring in a whole let less than the property is worth. Savvy buyers looking for investments buy cheap and sell high and make money. But regular people do not attend these sales and the sales are not well-advertised.
I am not a real estate lawyer and if you have obtained contrary advice from real estate lawyers who conduct partition sales, then I would defer to their expertise.