Use a standard AC transformer to get from 110/220V to 24Vac, then another (smaller, hand-wound?) transformer to get down to 10Vac. Also, from the 24Vac output, go through a diode bridge rectifier, a ripple cap, then into a linear regulator (LDO) to drop the 20-some volt DC signal down to +12Vdc for your display.
In all cases, you need to get from 110/220 Vac to 10Vac and 12Vdc. It's easiest to convert AC to AC, then AC to DC. It's much more complex to convert DC back into AC, or low voltage DC to a higher voltage DC.