1000 Watt Solar Panel
If you have a coffee pot that uses 1000 watts and you leave it on for one hour, it uses 1 kwh, right?
How many watts would a Solar Panel have to be rated for if the panel 'ran' at full for 10 hours a day in order to power the coffee pot that was left one for 5 hours a day?
You didn't say "rated for 1000 watts", you said "uses 1000 watts". Anyway, ignoring the example you gave, 1000 watts for one hour is
1 KWh.
Actually your whole question sounds theoretical, since you specify that the solar panel runs at full capacity for 10 hours and this is impossible.
The biggest problem with your question, theoretical or not, is that you can't run a load at 1000 W off of a source that only supplies 500 W.
You'd have to have a battery to store the 5 hours of Solar Panel Output before the load started running for 5 hours, and then having the panel and battery together supplying the load.