yes,hyper hypothyroidism can be cure without surgery.

Radioactive iodine is the most widely-recommended permanent treatment of hyperthyroidism. This treatment takes advantage of the fact that thyroid cells are the only cells in the body which have the ability to absorb iodine. In fact, thyroid hormones are experts at doing just that.

For patients with sustained forms of hyperthyroidism, such as Graves' disease or toxic nodular goiter, anti-thyroid medications are often used. The goal with this form of drug therapy is to prevent the thyroid from producing hormones