Attention is a relatively well defined and studied construct in experimental psychology and cognitive neuroscience. For instance, attention can be studied with respect to its spatial properties and temporal dynamics, and whether it is driven by "top-down" control or external stimulus (e.g., http://www.ncbi.nlm.nih.gov/pubmed/19575619). And brain imaging has characterized their neural correlates.
Engagement, on the other hand, is elusive. Here is a recent attempt to pin down the neural substrate of engagement:
Hi, in my diss "Engagement in educational games: An exploration of the interaction between game features, players perceptions and learning" I discussed the concepts of engagement, attention and effort, so you might want to look it up on the internet.