BJT Transistor question help here?
There is a sign error in the 1st equation.  The node voltage at the base is

$$V_B = -I_B\cdot R_B$$

so the correct KVL equation is:

$$-I_B\cdot R_B = V_{BE} + I_E \cdot R_E + \left(-V_{EE}\right)$$

The 2nd equation does not have the sign error.

If you do not have the value for \$V_{EE}\$, all you can do is provide the answer in terms of \$V_{EE}\$.  Deriving one of the DC bias equations, as you have done, may be all that is required.


  Also can you please show me the scheme of the common base transistor
  in this case?


It isn't clear to me what you're asking for since the canonical common base circuit schematic can be found in almost any transistor circuits textbook and is easily found with a Google search.