I have copied these following quotations from a study section of the Church of Jesus Christ of Latter Day Saints website explaining the identity of the God of the Old Testament:
Elder James E. Talmage explained the special significance Elohim has for Latter-day Saints:
“The name Elohim … is expressive of supreme or absolute exaltation and power. Elohim, as understood and used in the restored Church of Jesus Christ, is the name-title of God the Eternal Father, whose firstborn Son in the spirit is Jehovah—the Only Begotten in the flesh, Jesus Christ.” (Jesus the Christ, p. 38.)
Additionally the website says:
It is vital to remember the place of God the Father: He is the Father of our spirits (see Hebrews 12:9) and is our God. The existence of other Gods cannot alter that fact. He is the author and sponsor of the eternal plan of salvation. It is equally essential to note, however, that the agent by whom He administers His affairs on this earth is His Firstborn Son, known as Jehovah in the Old Testament.
It appears obvious that LDS views Elohim and Jehovah as two separate entities. Yet in Deuteronomy 4, in the midst of a passage wherein God is asserting yet again that there is no other God beside Him, we find:
Unto thee it was shewed, that thou mightest know that the LORD he is God; there is none else beside him. - Deuteronomy 4:35
And the Hebrew beneath this passage is:
859 [e] אַתָּה֙ ’at-tāh to you Pro-2ms 7200 [e] הָרְאֵ֣תָ hā-rə-’ê-ṯā it was shown V-Hofal-Perf-2ms 3045 [e] לָדַ֔עַת lā-ḏa-‘aṯ, that you might know Prep-l | V-Qal-Inf 3588 [e] כִּ֥י kî that Conj 3068 [e] יְהוָ֖ה Yah-weh Yahweh N-proper-ms 1931 [e] ה֣וּא hū He Pro-3ms 430 [e] הָאֱלֹהִ֑ים hā-’ĕ-lō-hîm; [is] God Art | N-mp 369 [e] אֵ֥ין ’ên [there is] none Adv 5750 [e] ע֖וֹד ‘ō-wḏ other Adv 905 [e] מִלְבַדּֽוֹ׃ mil-ḇad-dōw. besides Him Prep-m, Prep-l | N-msc | 3ms
In making the statement that there is no other God beside Him, God says, "Yahweh (Jehovah) He is Elohim."
How does LDS understand this statement that Jehovah and Elohim are one and the same?