Your lighting options for a 10g tank are somewhat limited. I don't think T5 and VHO are made under 24". PCs can be found, but I don't think I would keep an anemone under PC lighting. I run a 40w PC bulb (DIY) over a 10g tank that I use to quarantine corals, but that's just for short term observation. You may want to look into 70w MHs for nano tanks, but then heat may become an issue.
I would urge you to exercise extreme caution here. Anemones demand high water quality and stability (temperature and water chemistry). All of these things are difficult to maintain with such small water volumes.