Does anyone know if it is possible to power an electric fireplace & blower with only solar energy?
Yes, it is possible even if it has heating elements. It sounds as if the Electric Fireplace has an electric heating element and a blower fan.
The higher the kilowatt rating of the connected load; the higher the cost to purchase and install a solar system to supply it.
A 50 watt system with Photo Voltaic module, batteries, controller, and inverter costs about $700.
A 600 watt system with Photo Voltaic module, batteries, controller, and inverter costs about $8,000.
Here is a good site which will further explain solar power.