Is it possible to separate 2 crowns that have been joined together?

Without seeing x-rays or photos, it is hard to guess on the beszt treatment. It is LIKELY best to extract both teeth now and place a temporary of some sort. If infection is present, a new implant will NOT stay, so once the bone has healed, then one or both implants can be placed.  After they are BOTH placed, then you can restore.However, if the space for implants is too small, you are better off with a single implant and having two crowns attached, called a cantilever.  Implants cannot be closer than 3 mm away from each other, and 1.5 mm for adjacent teeth.  You did not say upper or lower, so if this is the lower arch, you may not have room.

It can be done but is likely to cause an aesthetic issue.  Probably better to take both off and have the dentist make you A temporary crown for the one that you are keeping for now.  Good luck.  

To get the optimal aesthetic outcome it is best to do it at the same time. You can separate the crowns and do it one by one.  However, it will be more difficult to achieve an optimal esthetic outcome.   The two central Incisors are the center of your smile.  Don't compromise this part of your smile. Time the treatment properly so that you can maximize your benefits for both years and get the treatment you need. You may also want to see a good Endodontist. An Endodontist specializes in saving teeth with root canal treatment.  They may be able to retreat the tooth and save you from getting it extracted.    

There are several things to consider in this situation. First, doing 2 implants side by side in the front of the mouth is very challenging aesthetically.I would suggest asking if the root canals can be retreated or surgically be repaired. A consultation with an endodontist may give you options that your general dentist isn't aware of. The longer you can keep these teeth the better technology gets. You don't mention why the teeth need to be removed but I suggest getting an opinion from an endodontist and a restorative dentist who has a lot of experience restoring multiple implants in the front of the mouth. You may be able to break this up over several insurance benefits years but there may be steps that can't be separated and you will need to pay out of pocket. The question is what is the value of your smile? I hope this helps.