Jesus did not answer their question. He already had done so when He explained that He and the Father were One (cf. John 5:18). The paradox of His dying and living forever would become clear with His resurrection. [source][source][source]
Instead of answering, Jesus urged His hearers to walk in the light as long as they had it. If they would do that, the darkness would not overpower them when the light departed (cf. Isaiah 50:10). If they did not do that, they would be lost. They needed to believe in Him then, before the Cross. After the Cross, when the Light was no longer present with them, it would be harder for them to believe. If they believed, they would become sons of light, namely, people who display the ethical qualities of light (cf. Ephesians 5:8; 1 Thessalonians 5:5). [source][source][source]
"The Semitic idiom "sons of" describes men who possess the characteristics of what is said to be their "father". In our idiom, we should probably say "men of light", cf. our expression "a man of integrity"." [1][source]