It is one of the beauties of relativity that there is no need to consider whether a collision is elastic or inelastic. Because any loss in energy after collision is accounted by the resultant mass(es) via E=mc^2. So goes into increasing the masses of the products. What I like to ask is some reactions result in energy lost via heat, sound etc which does not go into increasing the mass of the resultant product. How does relativity account for that? Is the answer that it dosen't? It only tells you how much energy is absorbed after the collision which goes into increasing the mass of the product. This extra mass could then escape away from the product via friction, heat etc but the formuals in relativity doesn't tell you exactly how much goes where, it only tells you the (very) initial stage of increasing the mass of the product(s).