Give it some time before you purchase an anemone. First they are not plants, they are animals. They require very high levels of light and at the proper spectrum. Also your water must be in pristine condition and must remain that way. You can not have any quick shifts in your water parameters with an "immature" tank while housing an anemone.
What size tank is that 18 watt bulb going on? A bulb that size would barely be enough for a nano tank of only 1 gallon capacity. It will probably grow plants if they are in a very small tank with the bulb specifically designed for plant use. But there is no way you could raise an anemone with that lighting.
For anemones you need high intensity lighting. Three kinds are PC (power compact flourescent), VHO (very high output flourescent), and metal halide (the kind of lights that light up street corners at night). NO (normal output) bulbs aren't nearly powerful enough and that sounds like what you have.