Your backup does not contain the songs. You either have to download them all over again, one at a time, or if you are syncing with iTunes they should be in your iTunes library and available to sync back to the device when the iPad is connected to your computer, with the iPad selected on the left side under "devices" and after clicking on the Music Tab in the iTunes window on the right.
If you don't sync with or use iTunes, then you have no other choice other than to doawnload them all over again.