This question came up on Friday and was dealt with a bit more on Monday. The issue concerns whether or not Jesus Christ could sin, and whether or not the ability to sin has a bearing on one's ability to be tempted. This is the question of impeccability, and it has been answered in different ways in order to explain the data of Scripture and theology.
First, we know that Jesus was tempted. Second, we know that Jesus did not sin. Both are clear from Hebrews 4:15 - "we do not have a high priest who is unable to sympathize with our weaknesses, but one who in every respect has been tempted as we are, yet without sin" (ESV).
The Greek word for temptation here can refer either to tempting or to testing depending on the context. Jesus' temptations in the wilderness (Mt. 4:1-11) are brought to mind. It is the same term in James 1:13 - "Let no one say when he is tempted, 'I am being tempted by God,' for God cannot be tempted with evil, and he himself tempts no one" (ESV). Testing occurs when God allows situations that, when overcome, will strengthen character and faith (as the whole of James ch. 1 indicates). Temptation is to sin, which God never brings about.
So while one may be tempted from outside, it is their inner reaction that determines whether or not they will be led into sin (note that in James 1:14-15 temptation leads to sin, it is not sin itself). Jesus passed His tests because He never sinned. In Him is no sin (1 John 3:5), He did no sin (1 Pet. 2:22), and He knew no sin (2 Cor. 5:21).
But could Jesus have sinned? It is difficult to imagine how a divine person could actually sin (whether incarnate or not). A. W. Pink said it simply: "Christ was not only able to overcome temptation, but He was unable to be overcome by it." This response troubles some, for it seems to them that one who cannot sin cannot really be tempted. But this objection confuses the temptation/testing distinction made above. Satan can tempt Jesus with something that Jesus would not be tempted by. Jesus had no sin nature to be activated by evil offerings. As William G. T. Shedd said, "It is objected to the doctrine of Christ's impeccability that it is incompatible with his temptability. A person who cannot sin, it is said, cannot be tempted to sin. This is not correct; any more than it is correct to say that because an army cannot be conquered, it cannot be attacked."
True, Jesus was His own person with His own human nature and will. But a divine person is still divine whether or not He is joined to human nature. We must remember that Jesus Christ is God! As such He is unchanging (if Jesus could sin then, could He sin now?), omnipotent (can God be overcome by anything?), and omniscient (and so does not need top experience inner temptation in order to know what it is like for us).
So while Jesus' human nature gave His divine person the ability to eat, grow, and even to die, it did not give Him the ability to sin. "The ultimate decision of the person . . . was always in harmony with the decision of the divine nature." (Walvoord, The Impeccability of Christ).