10W?
P=IV = .35 * (24V-14V) = 3.5W. So use 5W resistors. 10V/.35A = 28 ohm for Red,
(14 v worse case for Red)
4V/.35A = 68 ohm for blue/green. P=4*.35 = 1.4W, use 3W.
Depending on your PWM setting from Arduino, power dissipated will be 1/255 to 255/255 of that.
Or use a high wattage rheostat for even more fine tuning of the light levels
Say a 50 ohm resistor in series with 25 ohm 7.5W rheostat if you can find a place to get them - digikey has the part numbers to look for.
I would go with fixed resistors and PWM trimming, see how it works & add rheostats if its not quite what you want.
http://www.ohmite.com/catalog/pdf/rheostats_wirewound.pdf