Stage IV is the black end of the spectrum when it comes to curability. While it doesn't necessarily mean "death," it's generally labeled as terminal. The cancer tends to be very aggressive at this level, and harder to cure. Brain cancer itself is a hard thing to cure because it's usually a secondary cancer. If it is a secondary, the chemo treatment for the original cancer will usually be what works best. However, when it's the primary cancer, it's more difficult to treat.

Glioblastoma multiforme (GBM) is one of the deadliest forms of brain cancer. Jeph Loeb never stated what type, or stage, that Eddie's cancer was at. Considering the fact that it took him pretty fast, that would leave me to think that the cancer was very aggressive, and at an elevated stage. Knowing that he had cancer was one thing, but now that he knows it's terminal, it throws him into finding a way around death.

That's where Talia comes in. He was there the night Joker was taken. I'm taking a bit of creative license here, and saying that he saw her face that night. It's completely possible that he did, and that he remembered when he saw her picture in the paper, that she was the same woman who took the Joker. As Eddie said, Joker tells tales, and while they might not always believe him, fact is, Joker's probably telling the truth. It's a chance, and this cancer is going to kill him. He's willing to take the chance to find out if the Joker was making things up again, or if this was all true.
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