After you have chosen the battle’s Favor Card, the enemy immediately joins it. The enemy takes the top card from its deck and places it faceup into a new row above its last card played, called the Battle Row. You now resolve the battle using your card and the enemy’s card in its Battle Row.
These cards do not count toward the number of cards that the enemy plays in an Era for performing actions. However, their Active Runes still count toward the total it can use for Rune Actions and to boost actions. You will never fight the Invaders in a Solo Game, but instead only fight the Enemy Clan.