Dugger is right. I am pretty sure they are from the Caryophylliidae family, Paracyathus Stearnsi or Balanophyllia Elegans(Carribean Cup coral), similar to a sun coral or a dendro. Most that I have seen have been either clear or brownish in color. They are more like a solitary hard coral than an anenome(don't know why they are called this sometimes).No real special care, they will catch food with their tenticles, I don't think they contain zooxanthellae(not sure on this), so they should be fed zooplankton and meaty type foods if you want them to thrive, not just hang on. I wish I had them in my current tank, have had them years ago.
Matt