# What is the definition of Ecm in equation 7.10 of EC2?

In the old British standard we use a time dependent modulus of elasticity of concrete to calculate crack width, which is usually about half of the 28-day Ec for long term modulus. In Eurocode EN 1992-1-1:2004, from clause 3.1.3, it seems that Ecm is defined as the 28-day modulus of elasticity of concrete.

Is this definition correct, or should the formula be interpreted as Ecm(t) instead?

In a Eurocode context $E_{cm}(t)$ refers to the hardening of concrete until it reaches its 28-day strength. This is section 3.1.3(3). If you need to calculate a crack width at an early stage, you should probably use $E_{cm}(t)$ instead of $E_{cm}$, but this has nothing to do with the long term modulus.
Creep or long term effects is not included in $E_{cm}$ (refer for example section 3.1.4(3)). For equation this is accounted for by the factor $k_t$ and by the fact that you should account for creep in the calculation of the stresses in the cross section. This might be the confusing part: Even though equation (7.9) uses an elasticity modulus equal to $E_{cm}$, the steel stress in the same equation should be calculated using an elasticity modulus which is not equal to $E_{cm}$ but corrected for creep in accordance with section 3.1.4(3). Unless there are no long term loads, of course, in which case it gets a little simpler.