There is not a way to know exactly. I have my own theory; a lot of fuses will fry, breakers will trip and transformers will blow up but your solar system will likely be repairable. Breakers and fuses are designed to throw or blow when exposed to more current than they are rated for. Since a TV has a lot of electronic boards and no protection other than plastic and a breaker that's 100' away it will likely be toast. But lets think about solar components: Inverter is encased in a metal grounded chassis, charge controller-encased metal grounded chassis, DC power input is fused and GFPD is now part of National Electric Code.
One thing is for sure. If an EMP or flare is large enough to damage a solar system like the one above. Your TV, fridge and other equipment are definitely not gonna make it anyway. So, my best guess would be your good but keep a spare set of inverter motherboards and disconnect fuses just in case.
The toughest off grid inverter on the market is the Outback VFXR. The company provides excellent support after the warranty expires. In an off grid system; there are 3 pieces of equipment that matter. The inverter, charge controller and the batteries.
The Outback VFXR inverter has 3 boards that can be replaced in the event that the inverter goes bad. No soldering, just plug and play. It makes this inverter more "fixable" if something ever goes wrong. You can purchase a spare
set and your set for the long haul.
The Morningstar MPPT 600V charge controller is the most rugged on the market. All metal chassis and a basic user screen. No high tech thrills; just a solid charge controller. Other controllers have a lot of plastic and are designed for it's corresponding inverter manufacturer. Morningstar makes charge controllers.
There are 2 standard batteries DT Solar uses for an off grid installation.
Fullriver AGM batteries with a 7 year prorated warranty and Iron Edison Iron Phosphate. If you are a true prepper than the Iron Edison battery is likely the path you'll take. They are expensive but can last 30 years and are the absolute best on the market. With batteries you really do pay for what you get. Fullriver has the best warranty of the cheaper batteries and you'll likely need to replace them every 10 years.