Sorcery and witchcraft are explicitly forbidden by the Torah. Period. However, there are other methods of manipulating nature that do not fall into the category of "sorcery". For example, when a prophet or a tzaddik performs a miracle, they do it with G-d's implicit help and/or permission.
Mystically, the difference between these two methods (sorcery and G-d given miracles), is their sources. When G-d created the world, He created spiritual forces of purity and impurity, and forbade the latter (cf. Deuteronomy 30:19). (Judaism does not believe in the autonomy of evil). Sorcery draws from the powers of "impurity" in the world, and as such, is forbidden. Miracles and Practical Kabbalah draw from the forces of purity (kedusha) and are therefore permitted.
As far as King Solomon's control over demons, all the stories I've heard of that involve his using pure forces (specifically, names of G-d), to capture and bind them. From the Talmud, Gittin 68a:
...Solomon then sent Benaiahu son of Yehoyada, giving him a chain on with the [Divine] Name engraved and a ring with the Name engraved...
Oh, and David Livingston? I would say that he's wrong, but the fact is that English does not really differentiate between magic and miracle. They both defy nature, and when performed by a person, they fall under the blanket of the English word "magic". Rest assured, though, there is no magic or sorcery involved.
While your question is not really a duplicate as worded, most of this information is available on other questions on this site.
See further: Why is practical kabbalah not considered kishuf?, Did the prophets practice magic?