Yes you can. Other examples: He kept his composure when he was told that he'd failed his exams and then he got angry. She kept her composure when her husband said he was leaving. Later she cried. When they bought their house at the auction, they kept their composure until they got into their car.

"He accepted their problems with composure and she with equanimity."

"Inspite of her shouting loudly at him, he managed to retain his composure."

It might sound a little weird to leave the sentence as is. You would want to explain the situation as in Jura's examples.