Sakra, the last surviving princess of a fallen kingdom, is being hunted down for the power of Ambrosia she possesses - the ability to grant divine strength, but only to a human. With no human companion, she decides to summon one from another world in a desperate attempt to find a knight to protect her, but the man who answers her call is less than what she had hoped for.

From AnimeSigma:
One day while Shirou was delivering a secret weapon to his colleague, he met Amane Mao, a super strong girl who is capable of lifting cars. Before they knew it, an ERROR, a monster that struck Old Tokyo 14 years ago, reappeared and started on a rampage. While he was arguing with his colleague over the use of the super weapon to save civilians, his colleague was blown away and died. Faced with death, Shirou had no choice but to combine with Mao with the super weapon and destroy the ERROR.

From Tokyopop:
Yuuichi Tate is overjoyed: He gets to go to a brand new high school. Of course, then he just happens to find out the school he choose is under frequent attack by strange creatures called ''Orphans'', and the school set up a special task force of female members called ''HiME''s, using various elements as their powers, to battle these invaders. That's not all, though. Each member of the HiME task force has their own, unique ''Key'', another person whom, upon being discovered, can team up with the HiME to create a ''Child'', a combative unit specifically needed to effectively battle these Orphans. And with Yuuichi's luck, he just happens to find out he's not just the ''Key'' for one of the HiMEs, but for two... Two highly competitive, rival schoolgirls. And that's only the start of the trouble.

Set three months after the first series.

The St. Mikhailov Academy student Oribe Mafuyu comes across a mysterious silver haired boy named Sasha. He is a Qwaser, a being that draws power from Soma and is able to manipulate a specific element. And now, in the 21st century, the mystery revolving around an Icon turns the academy into the battlegrounds for the fight between the Qwaser!