The key here is E Major Lydian. E - F# - G# - A# - B - C# - D# - E.
Inversions come into play when you want to replace the root with another note within the chord. So say we have the triad E Major4.
Root position would be E - A# - B. 1st inversion would be A# - B - E. 2nd inversion would be B - E - A#.