I've read that the Tietze's extension theorem was still valid for continuous applications from a closed subspace of a normal topological space to a contractible topological manifold (understood as Hausdorf and 2nd countable).

But I can't find any clear reference for this result.

What I have found is that the theorem generalize to applications from a normal space to an Absolute Retract (but for which family ? Normal spaces ? Metric spaces ? both ?), that manifolds are ANR (Abolute Neighbourhood Retract, once again for which family of spaces ?), and that Contractible ANR implies AR. Is this correct ?

Is there a direct proof somewhere that Tietze generalizes to contractible manifolds ?

PS: it is not a research-level question, but I can't get any answer on MathStackExchange... sorry.