Obviously you are going to have to add something. You don't make any mention of how configurable the +10V supply is. For instance if you could convert the 10V to say 13V, you could use a linear regulator to convert the +13 to +3V. That node would be your reference ground. Now converting 13V to 3V if there is much current will make lots of heat, something to consider.
The difference between the +13V and the +3V (reference ground) is +10V. There is a problem with this method if your +10V uses much current is that the +3V will start to increase unless you shunt it with additional load, that is more load on the +-3V supply rail.
A very simple slam dunk solution is to buy a regulator known as a buck-boost, which is actually a positive to negative converter. You can get theses cheap, a few bucks. This is what I would do. It takes up perhaps 1 square inch of board space.
The AC/DC solution with bridge diodes will work except it isn't regulated and requires a lot of 120Hz filtering, big bulky components.
