The problem the Author is refering to in this quote is the one that, to David Lurie atleast, sex has been complicated by the issues of love, the idea that one cannot have sex without being in love. However, David Lurie simply wants to satisfy his sexual urges/needs , he doesn't want a relationship and all the "complications" that come with it. By sleeping with a prostitute, he solves the issue for he doesn't need to love the prostitute, and neither does the prostitute love him. He wants affection during the act, clearly, but nothing more. He doesn't want a relationship, he doesn't want to see Soraya after or outside the room where they engage. Also, Lurie is rather old and men of his age tend to have a harder time with sexual relationships, older women tend to be less sexually active and to traditional standards, less attractive. With a prostitute, he may have sex with younger, more attractive women as he pleases. The third point is the chase. He doesn't want to pursue women in order to solely sleep with them. This is time-consuming, tiring, frustrating and essentially pointless when he can have a prostitute without all the fuss. To him this is ideal, and he has solved the problem. He hasn't, however, since he starts developing more of an affection for soraya, and she clearly doesn't feel the same way. He also pursues Melanie, sleeps with her, and complicates his life dramatically by doing so.