The total energy required to power the load per day is 100 Watts times 24 Hours, or 2400 Watt-hours. Since the batteries can only be charged during sunlight, the solar panel must provide enough energy to run the load and charge the batteries during that 8 hour period, in other words, to provide the total daily energy during one 8-hour period. 2400 Watt-hours divided by 8 hours is 300 Watts. Therefore, the solar panel must provide 300 Watts -- excluding battery inefficiency, battery charge/discharge rate, and other losses and issues, of course.
The batteries must provide 100 Watts, or, assuming 120V, 100/120=.8 Amps. For 16 hours (number of discharge hours), that is .8 * 16 = 12.8 Ahrs -- also assuming linear discharge, independent of discharge rate.
Those are ideal minimum requirements. Of course, this is not the ideal world. You don't discharge a battery to zero energy just before the sun comes up, so you pick batteries that have considerably greater capacity than 12.8 Ahrs. You also don't pick a solar panel that has just enough output to charge the batteries to minimum charge and power the load before the sun goes down, so you pick one having considerably greater output.
The batteries must also be capable of being charged to capacity faster (8 Hrs) than that same capacity is diminished (16 Hrs) using twice the charging current that it is discharged at. I don't know if that is possible.