It's an extremely rare scale. It's what you call an "imaginary key signature", one that is there in theory, but isn't all that practical -- seeing as you could just compose in F major. However...
E# Major is a scale with 3 sharps (E, A, & B) and 4 double sharps (F, G, C, & D) in the key signature.
[ The double sharp symbol loosely resembles a lowercase "x". ]
So, the scale goes as follows:
E sharp (E #), F double sharp (F x), G double sharp (G x), A sharp (A #), B sharp (B #), C double sharp (C x), D double sharp (D x), E sharp (E #)
I hope this helped.
E F sharp G sharp A B C sharp D sharp E
The half steps in an E major scale are from Gis / G-sharp (enharmonically, As / A-flat) to A, and from Dis / D-sharp (enharmonically, Es / E-flat) to E.
G major, D major, E major, B major, F sharp major, F sharp minor, A sharp major, etc.
E Minor Scale has a key signature note of F-Sharp and with a G Major Scale.
E#
E F sharp G sharp A B C sharp D sharp E
E to F-sharp is one whole step. F-sharp is a major 3rd above D, so it's part of the D major scale.
The half steps in an E major scale are from Gis / G-sharp (enharmonically, As / A-flat) to A, and from Dis / D-sharp (enharmonically, Es / E-flat) to E.
G major, D major, E major, B major, F sharp major, F sharp minor, A sharp major, etc.
E Minor Scale has a key signature note of F-Sharp and with a G Major Scale.
E#
F sharp C sharp G sharp D sharp
A, B, C sharp, D, E, F sharp, G sharp, A
There are different rules. For major keys, the rule is this (by the way, # means sharp): C major scale- 0 sharps or flats G major scale- 1 sharp - F sharp D major scale- 2 sharps - F and C sharp A major scale- 3 sharps - F, C, G sharp E major scale- 4 sharps - F, C, G, D sharp B major scale- 5 sharps - F, C, G, D, A sharp F# major scale- 6 sharps - F, C, G, D, A, E sharp C# major scale - 7 sharps - F, C, G, D, A, E, B sharp. For major keys with flats: F major scale - 1 flat - B flat B flat major scale - 2 flats - B, E flat E flat major scale - 3 flats - B, E, A flat A flat major scale - 4 flats - B, E, A, D flat D flat major scale - 5 flats - B, E, A, D, G flat G flat major scale - 6 flats - B, E, A, D, G, C flat C flat major scale - 7 flats - B, E, A, D, G, C, F flat So as you might have noticed, in increasing order of sharps it is: F, C, G, D, A, E, B. And the increasing order of flats is B, E, A, D, G, C, F. If you notice the order of sharps is the opposite of the order of flats.
The D Major scale has two sharps, F and C. The notes in this scale are D, E F sharp, G, A, B, C sharp, D.
The key of 'E' major is the 5th key in the circle of 5ths, meaning it would have 4 sharps. F sharp, C sharp, G sharp and D sharp. Obviously since it is an E major scale, it starts on E, then F sharp, G sharp, A, B, C sharp, D sharp and E again. If you are talking about 'E' minor, the relative major is G, which has 1 sharp: F sharp. You would start an 'E' minor natural scale once again on 'E', then go to F sharp, g, a, b, c, d and e.
The pattern is up five scale notes when a new sharp is added to the new scale's seventh degree, if this was A major you just count five steps up in the A scale which will bring you to E. E major is the answer.