Yay Math Time!
Assuming a perfectly insulated pool, 0-ohm connectors, wires, etc.
Assuming that your inlet water temperature (ground/city water) is 50F (10C)
Assuming that your desired pool temp is 86F (30C)
Assuming that your pool is relatively small 12' x 24' x 48" (3.7m x 7.3m x 1.2m) and holds 4502 gallons of water (17041.9 Liters, 17041900mL)
1 Joule is one Watt-Second. Or in other words, one watt of energy expended in one second. And 4.184 joules of heat energy is needed to bring 1 gram of water (one cubic centimeter, or one mL) up one degree C.
So, we need to raise 17041900 mL of water 20 degrees. So math time!
To raise that much water just one degree would be:
17041900 x 4.184 = 71303309.6 watt-seconds.
To raise that much water 20 degrees would be 1,426,066,192 watt-seconds.
Now, of course you don't need to heat it 1 second, so let's say that we'll do it over the course of 5 days.
5 days = 432000 seconds
1426066192 watt-seconds / 432000 seconds = 3301 Watts.
Now that 3301 watts is continuous over those 5 days. And of course, that is assuming perfect ... well ... everything. Wires, heating elements, insulation, etc. No losses anywhere, which of course isn't realistic. However, 3.3KW is a somewhat realistic number, being roughly 14 amps at 240V, something that most households would be able to support.
(As a side note, that would be 396KWh consumed, and at about $0.12 / KWh, so it would cost you roughly $47 to heat your pool)
Okay, so lets take a look at your proposed power source, the Harbor Freight solar panel. The biggest one I could find was their 45-watt kit. So!
At 45W, how long would it take to heat that pool up? 31690359.82 seconds! That's only 366.78 days! But, realistically there are only about 14 hours of daylight during the summer, and to be fair, lets take only half of that to account for times when the sunlight isn't direct and the panel isn't outputting its full 45 watts, so about 7 hours of daylight a day.
End result? 1257.5 days, or roughly 3 1/2 years.
So...I don't think that your solar panel will actually heat that pool. Especially when you consider that almost everything in this system is "leaky". The pool water won't hold its heat forever due to imperfect insulation. The heater isn't 100% efficient either, nor is the electrical system involved.
Heck, just having it out in the sun will generate more heating power directly than doing the sun-> solar panel-> electricity-> heater route.