use of like following a substantive

Karim,

This is a great question, and not only are most people confused about how to hyphenate compound adjectives like this, but you will find different sets of rules in different grammar books. 

Here is one set of rules:

When the compound adjective comes before the noun or substantive that it modifies, use hyphens: a little-appreciated skill; a soon-to-be-married woman. But when the compound adjective comes after the noun or substantive that it modifies, drop the hyphens: a skill little appreciated; a woman soon to be married.

By this set of rules, because trance-like comes before the noun it modifies, experience, it should be hyphenated.  If the sentence were The experience was trance like, then no hyphens should be used.

However, as I said already, there is little consensus on hyphenation, and to my eyes  The experience was trance-like looks equally correct.

The good news is that most people would agree that in your sentence, trance-like should be hyphenated.