The adjective matter-of-fact is hyphenated and describes something or someone as having little to no dramatic emotion when speaking about potentially upsetting things. Note that this does not mean a lack of all emotion, but it means that the individual is not letting his or her emotions get the better of him or her.
The adverb form is matter-of-factly and the noun form is matter-of-factness.
An alternate noun form is matter of fact. This is used for things that are not opinion or up for discussion. Matters of fact are true and not guesses.
It should be noted here that the phrase matter of fact and matter of law can be specific to the legal realm. It is a designation for things that are under the judgment of a jury or the judge. Matters of law are for the judge to rule on, such as motions in a trial. Matters of fact are for the jury to decide, such as whether or not someone is guilty of a crime based on the evidence collected.
Examples
The long-shot candidate for the Democratic presidential nomination, in a matter-of-fact tone, typically reels off dry statistics about the rich getting richer while the middle class gets poorer. [The Wall Street Journal]
“We’re in the third global ukulele resurgence,” he said, matter-of-factly during an interview. [Alaska Highway News]
Describing the experience of being in hospital with his mother as doctors tried unsuccessfully to resuscitate her, he visibly deflates, though takes me through the events with a determined matter-of-factness. [The Guardian]