Experience

Earning Experience
In Card Hunter, characters level up by gaining  experience points (XP) after completing an adventure. The amount of XP earned is calculated as below.

Compare your character's level to the adventure's level, and if you are:

As an example: Suppose character A is at level 10 with 1 XP, and character B is at level 9 with 19 XP. Character A gains 4 XP from a level 9 adventure while character B gains 10 XP. Thus:

character A's XP = 1 + 4 = 5 XP at level 10 

character B's XP = 19 + 10 = level-up to 10 with 9 XP 

''' Due to the XP pattern, do not be surprised if party characters level up at different speeds. '''

Exception
Quest are unlocked after completing the single player campaign. No XP is awarded for completion of Quests.

Credits
http://forums.cardhunter.com/threads/could-we-be-told-the-xp-gain-numerically-not-just-shown-it-by-animation.572/#post-7668