The element that has oxidation numbers of +1 and -1 is hydrogen (H).

Here's why:

* +1 oxidation state: Hydrogen typically has a +1 oxidation state when it's bonded to nonmetals, like in water (H₂O) or hydrochloric acid (HCl). In these cases, hydrogen loses an electron to form a positive ion (H⁺).

* -1 oxidation state: Hydrogen has a -1 oxidation state when it's bonded to metals, such as in sodium hydride (NaH) or lithium hydride (LiH). Here, hydrogen gains an electron to form a negative ion (H⁻).

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