You would need 18 hour run time for vegging right? So your 7. 8kw load over 18 hours is 140.4 kwh. Where I am at, we would get about 4.5 hours of sun on average over the year so that would mean you need roughly a 31.2 kw solar array to generate that amount of kwh per day. However if you are running this year-round, consider designing for worse case sun. For me it would be 2-2.5 hours so that now means you need even more solar, more like 56kw. The solar panels don't run your loads, the batteries do. The solar charges the batteries through a charge controller which is separate or integrated into the inverter. To carry your load just off batteries, assuming a 48V battery bank, you would need 2,925 amp hours. That is just for 1 day. If this is all mission critical, a generator would be a must IMO. Having one will also allow you to reduce your solar array and battery sizes.
Check out Sol Ark inverters. They are compatible with many battery options and are solid inverters.