What is the ruling on selling a single gold earring, possessing its price, and then giving its original owner a sum greater than its price after he becomes aware of it?

This golden ring is considered a "found item" (luqata), and the duty of the finder is to announce it for a full year. If its owner does not appear, then the finder is permitted to take possession of it, while guaranteeing its value to the owner whenever he comes to claim it. You have erred by not announcing it and by selling it before announcing it. Since you sold it and gave its value to its owner, your duty now is to repent. You are not required to return more than its value, unless the ring has a counterpart [i.e., a similar item of the same kind that can be returned instead of its value], in which case the counterpart must be returned.