Darby Bible Translation says the following at John 14.10 (Brackets his):
"Believest thou not that I [am] in the Father, and that the Father is in me? The words which I speak to you I do not speak from myself; but the Father who abides in me, he does the works."
The words in bold reflect the Greek literally. Thus, a translator who seeks to stick closely to the original document, will do no wrong by rendering word-for-word in the text. In this group of literal Bibles we can include the Darby Bible, KJV, Young's Literal NT and the New American Standard Bible.
So what's wrong in rendering literally in the above verse? Let's imagine a 13 year old asking his/her parents what those words in bold above actually mean. Trinitarian parents in the western world would probably be tempted at once to explain the words on the assumption that Jesus is God. It is generally acknowledged that the Trinity dogma as understood today was not tied to Scripture until a few centuries later. Hence, it is important not to convey a posterior thought of another era to Jesus' sayings of the First-Century.
Jesus as a Jew fully sustained the Shema belief found at Mark 12.29:
"“The most important one [commandment],” answered Jesus, “is this: ‘Hear, O Israel: The Lord our God, the Lord is one."
Jesus' words at John14.10 are not a tribute to the complexity of the trinity doctrine. Rather it is a tribute to the "unity" existing between the Father and the Sent Son. Nothing more!
Eugene Nida and Barclay Newman, two scholars who worked on the UBS Handbook Series New Testament (20 vols.) for Bible translators, explained the meaning of Jesus' words at John 14.10:
"The meaning of [I am in the Father and the Father is in me] may be expressed by translating ‘I am one with the Father, and the Father is one with me.’....In some languages ‘my Father is united with me, and I am united with my Father’ or ‘my Father and I are just one as though we were one.’....The Father, who remains in me, does his own work is a fairly literal rendering of the Greek text. These words indicate that Jesus' miracles were not accomplished by his own power or initiative (see 8.28); rather, they reveal his union with the Father. A number of translators attempt a dynamic translation; NEB has ‘it is the Father who dwells in me doing his own work’; NAB ‘it is the Father who lives in me accomplishing his works’; Mft ‘it is the Father who remains ever in me, who is performing his own deeds’; Gdsp ‘but the Father who is united with me is dong these things himself.’
However, it may be difficult to speak of the Father ‘doing his own work.’ The reference is obviously very broad, for it includes both miracles and sayings. Sometimes one can employ such an expression as ‘my Father who remains in me causes these happenings.’ But in other instances a more satisfactory rendering may be ‘...does what he decides to do.’ Such rendering indicates clearly that the agency and the initiative rest with God."
However, since the Trinity doctrine is prevalent within the religious world of Christendom, modern Bible readers amazingly prefer the literal wording as indicated in their so-called "contemporary" English versions. They may not realize that the words in bold above are Greek words dressed with English ones. It is the duty of the translator to employ English idioms in a contemporary version instead of Greek ones.
In sum, John 14.10 is not a "mistranslation" per se in most English versions. They reflect the Greek wording with English replacements. Nevertheless, most English versions claiming to be "contemporary" fail in providing a thought-for-thought translation in John 14.10 by conveniently sticking to Greek idiom. So a better subject title would have been: "The mishandling of John 14.10."