First, engineering was at first thought to be a matter of building roads and bridges and similar structures...either for war ( ergo a military engineer, who'd also be building forts and digging trenches) or not ( civil engineer) .Generally speaking, there was a French method and an English method. If you were French, from early in the 18th c. there would be a school , the National School of Bridges and Roads and you'd be trained in geometry, surveying, hydraulics, etc. If you were English, you'd typically apprentice with somebody. One example would be John Brindley who apprenticed with a millwright, a builder/designer of watermills and all the land and water-scaping that was required for them. From this training , Brindley would go on to build the famous Duke of Bridgewater's canal.

Though the line was blurry, English engineers tended to be less scholastic, more pragmatic. French engineers would do elaborate and painstaking calculations of arches, spans. English ones tended to work a little more from experience. In the US, the center of engineering education was the military academy of West Point, and it was pretty much in the French school.

When you get into the Industrial Revolution in the late 18th c., engineers become more and more interested in machine and industrial design, with figures like John Smeaton creating the field of mechanical engineering, and there were stronger ties to scientists, and scientific research.

After the Napoleonic Wars, the English would realize they needed a school for military engineering, and one was created.

A rather hagiographic but still useful book on early English engineers is Samuel Smiles' Lives of the Engineers

Would engineering even be a profession in the mid-late 18th century England?