First, the historical background from something I just found.
On April 24, 1946, the JTA reported
U.S. Government Not Ready to Recognize Transjordan Independence, Says Byrnes
"Byrnes" was Secretary of State James F. Byrnes and he had
announced that the State Department considers that "it would be premature for this Government to take any decision at the present time with respect to the question of its recognition of Transjordan as an independent state."
Britain had recenting granted Transjordan its independence.
In a letter to Senator Francis J. Myers of Pennsylvania, who had written to the State Department protesting the granting of independence to Transjordan and inquiring about the American attitude. The text of the Byrnes letter, which was made public today by the State Department, reviews the background of the Transjordan affair and points out that Article 25 of the Palestine Mandate distinguishes between the lands west and those east of the Jordan River...Quoting Article 7, which stipulates against modification of the Mandate without United States assent, he declare[d]...This article, however, renders it possible for this Government to decline to recognize the validity of the application to American rights and interests, as defined by the [1924 Anglo-American] convention, of any modification of the Mandate unless such modification has been assented to by the Government of the United States," Byrnes stressed...There has been, therefore, a differentiation in the treatment of Transjordan and Palestine since 1923," Byrnes declared, "formally approved by the Council of the League of Nations in September 1922 and tacitly approved by the Government of the United States when it signed and ratified the Convention of December 3, 1924."
What this means, and I have pointed it out previously, here and here, is that the 1922 League of Nations Mandate for Palestine linked the west and east sides of the Jordan River even though it suspended or postponed the terms of the Balfour Declaration as regards the reconstitution of the Jewish National home in the area east of the river.
Therefore, in 1946, when Transjordan became "independent", the claim was made, and adopted by the State Department, that until the "Palestine" issue was resolved, Jordan was still a part of the Mandate's overstructure and, for example, could not become a member of the United Nations.
And as I have extrapolated, Jordan still must be, in some way, part and parcel of the "solution" of the conflict that Israel has been caught up in.
The solution is indeed one of a "two-state" definition - but not as most people presume.