Let \( f(z) = z + e^{-z} \). Prove that, for any real number \( \lambda > 1 \), there exists a unique \( w \in H = \{ z \in \mathbb{C} : \text{Re } z > 0 \} \) such that \( f(w) = \lambda \).
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Let \( f(z) = z + e^{-z} \). Prove that, for any real number \( \lambda > 1 \), there exists a unique \( w \in H = \{ z \in \mathbb{C} : \text{Re } z > 0 \} \) such that \( f(w) = \lambda \).