A man asked Jesus "How can I have Eternal Life?"
To which Jesus said "Obey the commandments."

Does this mean there is another way, besides belief in Jesus, to be granted eternal life?

As you may recall, Jesus told that man "There is one thing you lack ..." And it seems inevitable that anyone attempting to establish a righteousness on their own by obedience to the 10 commands, will find out that there is always "one thing you lack..."

Therefore let us be confident to say that no man will be declared righteous in the sight of God by obedience to the Law.

This does not sum up all aspects of the Law, but it is a useful story about this topic:

A clutz brags about his coordination. However, his confidence is based on ignorance, because all he does is sit around all day upon his hands.
Thus, a wise man (seeing the problem) tells the clutz to get up and fetch some dishes in the kitchen ... and as predicted a crash indicates the inevitable ... the clutz dropped all the dishes! So much for his coordination.
So the wise man gave a command that would reveal to the clutz a problem that he was either unaware of or had otherwise denied ... that indeed he was not coordinated.

And so we read:

Ro 5:20
And the Torah came into the picture so that the offence would proliferate; but where sin proliferated, grace proliferated even more.

Does not a plumb line indicate where a wall is crooked? Indeed it does.
Does the plumb line MAKE the wall straight? It CANNOT.
Yet once straight, the plumb line will match the wall that was made straight by Another!

I am not talking about mere walls and plumb lines, am I? I speak of man and the Law ... and Another (the Lord) Who makes straight each of us that the Law shows as crooked.

Lets agree that the Moral Law that condemns us is not the essential source by which to mend us. It shows our wickedness, by contrast, and it validates the fruit of the Spirit by comparison.