I did backpacking around Europe about 20 years ago

and hell 10 grand sounds more than enough. Most of your money will go on accommodation so if you can get into hostels and campsites you'll save a bundle. Also Europe has a whole load of currencies to contend with, so checking the value of the $ against the countries you'll be going to is another must but most countries will be in the Euro.
Also you need to think of the weather and when you'll be travelling as the weather between northern and southern Europe is like north to south USA.