How is the divinity of Jesus defended in light of Philippians 2:9 ("God exalted him") and Matthew 28:18?

It was the choice of Jesus Christ to empty himself. Jesus Christ freely emptied himself (ekenosen) (Phil. 2:7). That is to say, Christ freely gave himself for us through the incarnation in order to die on the cross.

being born in the likeness of human beings, and having found in form "as a man" (οσ ανθροπον), he humbled himself and obeyed, to the point of dying on a cross (Philippians 2:7c, 8).

After dying on the cross, Jesus was raised from the dead and God the Father freely gave (echarisato) the name above every name to Jesus.

So that at the name of Jesus, every knee will bow --- in heaven, on earth and under the earth and every tongue will confess Jesus is Lord to the glory of God the Father. (Philippians 2:9-11).

Jesus was already existing as a divine being (one who had a divine nature: God by essence) in verse 6 when Paul stated that Jesus was existing in the form of God and had equality with God. The God being referenced here was the Father and Jesus had the nature of his Father (showing that Jesus was the Son) and that Jesus was equal with the Father (in position, as Kyrios) as evident in his self-emptying wherein He chose to add to himself (take upon himself - Greek: λαβον) the form of inequality (i.e. the form of a slave). Then Jesus was highly exalted by the Father to reveal the previous lofty status of Jesus stated in verse 6. Jesus was elevated into a high position after Jesus himself brought himself into a lower position when he emptied himself (through the incarnation and crucifixion in vv. 7-8).

There are two ways the divinity of Jesus Christ is defended in the Carmen Christi:

(1) Jesus Christ was previously existing in the form of God (a non-human form) in verse 6 and he was already in that divine form prior to becoming human in verse 7-8. See also Galatians 1:1, 1:11-12, cf. 4:4 where Jesus was pre-existing as non-human prior to being born of a woman

(2) Paul applied a very monotheistic passage (Isaiah 45:23) to Jesus, citing Jesus as the fulfillment of that eschatological event in Isaiah wherein everyone will bow to Kyrios = YHWH. Kyrios (master, lord) was the substitute for the Tetragrammaton (YHWH) used in the Greek copies of the Old Testament.

John 1:1 In the beginning was the Word, and the Word was with God, and the Word was God... 14 And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.

Proverbs 8:22 The LORD possessed me in the beginning of his way, before his works of old.

John 16:28 I came forth from the Father, and am come into the world: again, I leave the world, and go to the Father.

Hebrews 1:8 But unto the Son he saith, Thy throne, O God, is for ever and ever: a sceptre of righteousness is the sceptre of thy kingdom.

Yeshua gave up certain "God features" to take on humanity, when he went back he was exalted back to full "God-hood" so to speak, and given full authority due to what he accomplished for heaven and earth.

In agreement with what Nigel J has written, but in addition to him, I add what I think conclusively shows Phil 2:9, in context, is saying that Jesus is God, and thus both God and man, two distinct natures in one person.

9 Wherefore God also hath highly exalted him, and given him a name which is above every name: 10 That at the name of Jesus every knee should bow, of things in heaven, and things in earth, and things under the earth; 11 And that every tongue should confess that Jesus Christ is Lord, to the glory of God the Father. (Phil 2:9-11)

Here the Apostle is making use of Isaiah 45:21-23 :-

21 Tell ye, and bring them near; yea, let them take counsel together: who hath declared this from ancient time? who hath told it from that time? have not I the LORD? and there is no God else beside me; a just God and a Saviour; there is none beside me. 22 Look unto me, and be ye saved, all the ends of the earth: for I am God, and there is none else. 23 I have sworn by myself, the word is gone out of my mouth in righteousness, and shall not return, That unto me every knee shall bow, every tongue shall swear. (KJV)

or let me quote from the Watchtower version which is here even more clear :-

21 ".... Is it not I, Jehovah, besides whom there is no other God; a righteous God and a Saviour, there being none excepting me? 23 Turn to me and be saved, all YOU at the ends of the earth, for I am God, and there is no one else. 23 By my own self I have sworn, - out of my own mouth in righteousness the word has gone forth, so that it will not return - that unto me every knee will bend down, every tongue will swear, 24 saying, surely in Jehovah there are full righteousness and strength. (NWT, emboldening mine.)

So here it is being prophesied that they will swear by the name of Jehovah. Yet in Phil 2:9-11 they will bend the knee to and swear by the name of Jesus.

So Jesus is that "Jehovah, besides whom there is no other God". (Isaiah 45:21, NWT).

It can also be pointed out that often in the New Testament the term "God" refers exclusively to "God the Father".

"The grace of our Lord Jesus Christ, and the love of God, and the fellowship of the Holy Spirit be with you all. Amen" (2 Cor 13:14)

(This is on Paul's assumption, of course, that the all being addressed love the Lord Jesus Christ (1 Cor 16:22)).