If you mean the first, neither needs the other; rather, neither requires the other to be its agent. Nor does it follow that both are necessary existents in the sense that each is necessarily existent in itself and brings contingent beings into existence.

If it is said:
“Each is a necessary existent in the sense that it has no creator,”

the reply is:
“Yes, but we do not concede that there cannot be more than one thing designated a ‘necessary existent’ under this definition. Multiplicity is impossible only under the first definition. The proofs establish that the creator of contingent beings is one Lord; they do not establish the negation of His attributes. Rather, each of His inseparable attributes is eternal and beginningless; its nonexistence is impossible, and it has no agent. If this meaning is expressed by calling it a ‘necessary existent,’ that is true. But if ‘necessary existent’ means something that is not inseparably linked to anything else, then neither the essence alone nor the attributes are necessarily existent. Rather, the Necessary Existent is the essence qualified by its inseparable attributes—especially since they themselves say that it necessarily entails its effect. Thus, this is all the more impossible on their own principles. It is already known that each of the essential attributes is inseparably linked to the others, and that the attributes are inseparably linked to the essence, without either creating the other.”

If you say:
“Each needs the other in the sense that it is inseparably linked to it,”

being inseparably linked does not entail being an effect.

[The second way]

This is the second answer, namely, to ask:
“What do you mean by ‘necessary existent’?”