I ask about if the intent is to remarry...since if you do? This really is no more than a "bump in the road"
Again, I am assuming this was an error on his part (and not planned). Since that is the case, if you annul your current marriage and then remarry? As far as your marriage goes, this will not be an issue.
There is a cost...you have to file for annulment. There is some cost associated with this. You can "do it yourself" and save money on a lawyer (so you just pay the filing fees). You can work with a service Like this one
and pay the cost for the service, which is typically much less than hiring a lawyer but requires you to do some of the work (like filing the documents). Or you can hire a lawyer and let them do all the work.
Then there is a cost to remarry (for the certificate and to pay the officiant if they charge).
But if you agree? You can be through this and remarried in a matter of weeks.
Now...if you do not agree to remarry...or can not agree to annul? Then it can get complex. Quick.
I suspect you have a good deal of property tied up in your marriage. If you can not agree to remarry, in order to recoup your share of the property you acquired together, you may have to sue him. There would be a cost here as well (to hire the attorney to sue him). But you have recourse...since this was not your fault, the law is on your side if you have to fight to protect any property you have a right to based on the fact you thought your marriage was valid.
But if you are working together to fix this problem ? Easy...get an annulment, then remarry...then you are set.
Next year, when you file your taxes you can send a copy of the annulment order in with your explanation on what happened...the IRS is not going to make you redo taxes at this point since when you filed you had a good faith belief you were married.