My previous answer, Especialidad en Enseñanza y Aprendizajes Escolares, looked good for the head of an ordinary school, but now we know it's a nursing school I think it's much more likely to be this. The head and deputy head of a nursing school are more likely to have nursing qualifications that graduate educational qualifications (though they might have the latter as well), and in particular if both the directora and the subdirectora have these initials, it would be quite a coincidence for them both to have one particular graduate teaching diploma that appears to exist at only one university. A further point is that there is a space between "E.E." and "A.E.", which I assumed was a mistake, but, if not, suggests that these are two pairs of initials rather than one set of four.

Taking all this into account, I think EE must stand for "Enfermera Especialista". AE is more tricky. It usually stands for "Auxiliar de Enfermería". However, I think it's more likely that it stands for "Administración y Educación", given that the head and deputy head of a nursing school clearly specialise in these areas. It is possible that both of them initially qualified as auxiliares and then went to on become especialistas (which means a licenciatura and then further study; see below). But in that case I don't think it's very likely they would mention the "A.E." part. However they certainly would if, as I believe, it stands for Administración y Educación.

Some references:

"Farmacología para Enfermeras
Area que programa: Enfermería
Dirigido a: LE, EE, EG, Y AE"
http://hospitalgea.salud.gob.mx/slideshow/enseñanza/cursos-d...

"El nivel de estudios fue categorizado como: auxiliar de enfermería (AE), enfermera(o) general (EG) o especialista (EE), y licenciada(o) en enfermería (LE)."
http://www.scielosp.org/scielo.php?script=sci_arttext&pid=S0...

"ENFERMERA ESPECIALISTA
FORMACIÓN ACADÉMICA: Licenciatura en enfermería y de uno a dos años de estudios de una especialidad en enfermería. [...]
FUNCIÓN SUSTANTIVA: Determinada por el área de especialización; asistencial, administrativa, docente o de investigación."
http://salud.edomex.gob.mx/html/Medica/ENFERMERIA. PERFILES ...

"10.- Nivel académico de enfermería obtenido
1 ) Auxiliar de Enfermería
2) Técnico en Enfermería
3) Enfermera General
4) Licenciado en Enfermería
[...]
13.- Área de práctica profesional
1) Administración y educación
2) Clínica
3) Consulta
4) Otras"
http://eprints.uanl.mx/6108/1/1080089074.PDF (p. 99)

Given that there is inevitably an element of doubt in this, I think it would be a good idea to try to confirm the meaning of these initials with the client, if possible.