The cache is not at the posted coordinates. The cache is within 3 km of the posted coordinates.
About Hadrian's Wall
Hadrian's Wall, also known as the Roman Wall, is a former defensive fortification of the Roman province of Britannia. It runs from Wallsend in the east to Bowness-on-Solway in the west covering the whole width of the island. In addition to the wall's defensive military role, its gates may have been customs posts. A significant portion of the wall still stands and can be followed on foot along the adjoining Hadrian's Wall Path. It is a designated UNESCO World Heritage Site
Hadrian's Wall marked the boundary between Roman Britannia and unconquered Caledonia to the north. The wall lies entirely within England and has never formed the Anglo-Scottish border, although this is a common misconception.
Source: Wikipedia
The Lesson
To find the final coordinates, you have to learn a lesson in history, and answer the following questions.
A = The wall was essentially abandoned when Hadrian died. Which year did he die? Second digit of this number.
B = When was Hadrian's wall designated as a UNESCO World heritage site? Last digit of this number.
C = X + Y + 1
D = When did work start on the wall? Last digit this number.
E = The digital root of the length of the wall in miles.
Now the difficult part - there were several forts along Hadrian's wall. The westernmost fort is X, and the easternmost fort is Y. Use these to calculate C.
Final is at N 43° 3A.40B' W 79° 42.CDE'