Both 真実 and 事実 means; fact,truth. So in Kanji Lesson I asked my teacher if there is any differences between them, he said yes but there was no time to explain.
Just use the kanji to break it down.
事 = thing;
実 = true. So it's a "true thing", "something that is true"; a fact as opposed to a false statement. Exs.
- 空は青いです → The sky is blue; this is a fact
- 太陽は東から昇り西に没する → The sun rises in the east and sets in the west; this is also a fact
- 事実無根 → (a) groundless (fact)
真 = true, real;
実 = true, truth. So this is truth as an abstract concept, as opposed to a lie.
- 真実を言え！ → Tell the truth
- 彼の言うことの真実性を疑う → I doubt the truth in what he says.