I have to write a formal essay about environmental issues. I want to write a sentence: "I can no longer hold the silence about this problem". Is it possible to say this? Or its better to say something like maintain/remain/keep my silence? Which one sounds more formal?
The idiomatic expression "keep silent" is already common:
I can no longer keep silent about this problem.
This is fine to use in your essay. Style guides do suggest you avoid using the personal pronoun "I" in formal essays, as it's redundant because the reader already knows it represents your personal opinion. It may be better to write it as a general recommendation for all of humanity:
We can no longer keep silent about this problem.
In more creative writing, you can say anything you want, and there's nothing wrong with "hold the silence", when placed in a context where it makes sense. The nuance it somewhat different and means "be silent" rather than "keep silent". It's something I might say when teaching mediation:
As you begin to focus inward, learn to hold the silence within you, calming your thoughts and letting your breath move in and out like the waves of the ocean.
If I wanted to use it as a creative variation on "keep silent", I would probably use "maintain" rather than "hold", and use a personal pronoun.
The fury rose within her, threatening to overcome her natural decorum. She could no longer maintain her silence about the problem -- she wanted to rage and scream and break everything that would satisfyingly shatter when thrown against the wall.