From my experience of jazz, solo phrases tend to a mish mash of diatonic scale and arpeggios, often linked using chromatic notes. Scales can also change regularly. Its very free, but you have to stop thinking like a classical musician! Maybe smoke a few joints of something, and loosen up. All the jazzers I knew had little theoretical knowledge. But they did have great ears, and the ability to 'think on their feet'.
I mean, half the chords in jazz are altered anyway, especially dominants. So just play what you think sounds good, and save the analysis for another day.
Or even better, dont bother. Then when you're a famous composer, kids can sit of internet forums and arguing over why theirs a Db rather than a D#!

Im convinced that more than one composers has done this in his years. Jerry Goldsmith and plenty of other film composers openly admit to simply penning what they 'hearing' in their heads.
But getting back on topic, the scale is E Melodic Minor with a chromatic passing note (D#). They use these in Jazz and Blues all the time. For example, the traditional Blues scale is a simple minor Pentatonic with a chromatic passing note between the third and fourth degrees.
SJ