There are a number of local operators who do that trip, chances are at least one of them will have leaflets etc., in your hotel. If not, just walk down the road a bit, and take your pick.

Welcome to HT ianjoanie

I have never been to Hurghada (no flights there from the frozen north ) however I can give you some information.

Yes you can get to Luxor and visit the Karnak Temple, Valley of the Kings etc from Hurghada, this is usually done as a coach tour as there are no direct flights from Hurghada to Luxor, this takes around 3.5 hours so is a very early start (5am ish) and late night. You can take either a 1 day tour or go for 2 days with an overnight stay in Luxor.

If you are travelling with a tour operator such as Thomson they will have excursions and these are the most expensive way of doing it, however you may prefer to book through your rep as I know many people feel more secure so please book with who you are most happy with.

Take a look at this excursion page from Thomson which gives you the costs and details. http://www.thomsonexcursions.co.uk/search-excursions/EGY/Egypt/001689/Red-Sea/000851/Hurghada/65/History-and-Culture.aspx

Your hotel may also have an excursion sales rep who is usually a bit cheaper than booking through your tour company.

The 3rd option is to use one of the local travel companies who are out in Hurghada, they will provide you with the same tour as your tour company but at a much cheaper cost.
As I mentioned I have never been to Hurghada however I been been to Luxor & Sharm many times and I am happy to book locally for any excursions I want to take and have always paid a lower price than our reps and have never had any problems.

Remember that your reps price is fixed with no room to haggle, if your hotel does excursions you can try and haggle the price down a little and local tour operators definitely try and get a bit off, there are a lot of good deals locally in resorts as they are all competing for your business.

A quick internet search has found this random selection which will give a bit of information however I would wait until you arrive and can shop around

Make sure this one is on the £ currency at top of page http://uk.memphistours.com/Egypt/Excursions-And-Attractions/Hurghada-Excursions

http://www.hurghadaexcursions.net/excursions-and-day-tours/bus-tours/74-day-excursion-by-road-to-luxor-east-a-west-banks-sightseeing-tours-from-hurghada.html

http://www.egypttoursportal.com/Egypt-Day-Trips-and-ExcursionsHurghada/Luxor-Day-Trip-from-Hurghada--/id_prod147

Graham