Who was the british prime minister in 1758?

In 1758 the British prime minister was Thomas Pelham-Holles, first Duke of Newcastle. His second term as PM had started in 1757. The term Secretary of State is applied to several senior ministers, e.g. Secretary of State for Education, Secretary of State for Defence, Secretary of State for Wales, etc.

If you are thinking of the American usage of the the person in charge of foreign relations the post didn't exist in 1758. There were two posts: Secretary of State for the Northern Department, who was responsible for relations with the protestant states of northern Europe, and Secretary of State for the Southern Department, who dealt with the Catholic and Muslim states. In 1758 these were respectively Robert Darcy, 4th Earl of Holdernesse (took office 1754) and William Pitt the Elder, (took office 1757).