Old Testament Ps 110:1 David says "The LORD [Jehovah/YHWH] says to my Lord [Adonai]: “Sit at my right hand, until I make your enemies your footstool.” 

David, in this Messianic Psalm, is referring to God in both terms. Both the "LORD" [Jehovah/YHWH] and my "Lord" [Adonai] are holy names for the One True God.

 Jehovah/YHWH is the divine name of the One True God as revealed to Moses in Exodus, while Adonai is also used only when referring to the One True God. Adonai became even more common when the divine name of God became regarded as too sacred to even speak. [Meanwhile, "adon" and "adoni" may be used as titles of respect for royal or distinguished persons.]

So, if both Jehovah/YHWH and Adonai are reserved for the One True God (of Abraham, Isaac and Jacob) and in Ps 110:1 David speaks of both as separate persons yet uses the name of God for each, then we can see that when Jesus says "The Father and I are one" in John 10:30 that He means it. This is not meant as a New Age interpretation, but it is literal. 

When Jesus says "...that you may know and believe that the Father is in Me, and I in Him" in John 10:38b, He means it. When Philip asks Jesus "Lord, show us the Father, and it is enough for us" and Jesus says "Have I been so long with you, and yet you have not come to know Me, Philip? He who has seen Me has seen the Father; how can you say, 'Show us the Father'?" He. Means. It. 

See also: Matthew 22: 41-46 "Jesus asked them a question, saying, 'What do you think about the Christ? Whose son is he?' They said to him, 'The son of David.' He said to them, 'How is it then that David, in the Spirit, calls him Lord, saying, "The Lord said to my Lord, 'Sit at my right hand, until I put your enemies under your feet'?  If then David calls him Lord, how is he his son?" And no one was able to answer him a word, nor from that day did anyone dare to ask him any more questions."

Psalm 68:20 says "Our God (El) is the God (El) of Salvation; and to God [Jehovah/YHWH] the Lord [Adonai] belong escapes from death." Once again we see here that both Jehovah/YHWH and Adonai are used for the same One True God. 

In the Old Testament scriptures, in Exodus 3:14 it states "and God said unto Moses 'I Am that I Am' and He said 'Thus shalt thou say unto the children of Israel 'I Am hath sent me unto you' ". In John 8:58b Jesus says "before Abraham was, I Am." This statement caused the crowds to want to stone Him. 

There is much more context and many more examples.

Please read the scriptures for yourself and sincerely pray for God to reveal His Truth. 

Jer 29:13 "You will seek Me and find Me when you search for Me with all your heart."