I have the following equation that i want to solve,
x*C -E -y = 0

Here, x and y are given; C and E are variables,
x’s size = (128,1),
C’s size = (1,2),
E’s size = (128,2),
y’s size = (128,2),

An important constraint other than the equation mentioned at first is that every row in E has to have the same value. That is E[0][0] = E[1][0] = E[2][0] = … = E[127][0] and
E[0][1] = E[2][1] = … = E[127][1]

How to frame the syntax for this in cvxpy (or cvx)? Answer mainly needed for cvxpy. Please help.

This is not the appropriate place for CVXPY assistance. You should be able to apply one or the other of the ideas I showed to CVXPY. If you need more specific CVXPY assistance, you will have to request assistance on one of the CVXPY support locations.