I'd be a bit suspicious of the solar charger. It says output in bright sunlight is 320mA. The supplied charger for the n810 has an output of 890mA, nearly 3 times as much. I've found that chargers with too little power can get the n810 to display 'charging' but the time left still goes down: at least that's my experience with both a USB charging cable and an AA cell charger when the cells aren't brand new.
So, it might work or it might just seem to charge without being effective.