Maybe you can do it. Just replace your sunglasses lenses with prescription reading lenses. And you'd better have an optician to do it. But if your sunglasses have a too big frames (that means need big lenses), prescription reading lenses may not available. So, you may have to buy another pair of prescription sunglasses. Or clip on sunglasses can also help you with prescription lenses for vision aids and dark lenses to shield eyes.
That depends on the type of curve of your sunglasses lenses. In fact, it is difficult to put prescription into the wrap around style frame sunglasses. Therefore I suggest you take your sunglasses to an optical store to have your prescription and sunglasses checked. The lab technician will know whether your sunglasses can made into prescription reading sunglasses or not. If they can't, you can buy a new pair of prescription reading sunglasses which won't cost you too much.