homomorphic encryption E(x+y)=E(x) . E(y)?
could you please tell me what is it that I'm missing ?


Typically, when we write $a \times b$, the operator $\times$ needn't be multiplication over the integers (or reals or complex numbers).  Instead, it is often some group/ring/field operation that is somehow analogous to the more common multiplication operations we all learned in grade school.

That's exactly what is happening here.  In this case, the elements $a, b$ (or, in this case, $E(x), E(y)$) are understood to be elements in the group $\mathbb{Z}^*_p$, and so the multiplication is done in that group.  That multiplication can be implemented by performing a standard integer multiplication, and then taking the result modulo $p$; writing that out explicitly gives your result.

So, why do we do such a short-hand? Are we lazy?  Well, partially, yes, we have no reason to clutter the equations with things that are well-understood.  On the other hand, sometimes we work with things, such as extension fields, or elliptic curve groups, which do not have such a simple "do a normal addition/multiplication and then fix things up" way of looking that things; trying to write things out explicitly in the 'grade-school approved notation' would be tricky...