What is the difference between category C, category C + E and category B + E ?
Essentially C means HGV, B means car, E means trailer. Once you have passed your test the appropriate category(s) will be added to your licence permitting you to drive that type of vehicle.
If your driving licence was issued prior to 1 January 1997 then you are entitled to tow with a car. Licences issued after that require you to pass the B + E trailer driving test to tow anything heavier than a light trailer such as a horsebox or medium to large caravan.
To tow with a lorry requires you to pass the C + E HGV driving test.