Molality of the solution prepared from a hydrated salt
Let's denote a hydrated salt as $\ce{M_pA_q*xH2O}$ ($\ce{M}$ – metal, $\ce{A}$ – anion). Then molality $b$ of the aqueous solution of $\ce{M_pA_q}$ is defined as

$$b=\frac{n(\ce{M_pA_q})}{m_\mathrm{tot}(\ce{H2O})}\, ,\label{eq:1}\tag{1}$$

where $n(\ce{M_pA_q})$ – amount of water-free salt; $m_\mathrm{tot}(\ce{H2O})$ – total mass of water.

Note that the amounts of the hydrated and the water-free salt are equal:

$$n(\ce{M_pA_q})=n(\ce{M_pA_q*xH2O})=\frac{m(\ce{M_pA_q*xH2O})}{M(\ce{M_pA_q*xH2O})}\, ,\label{eq:2}\tag{2}$$

where $M$ – molar mass.

Total amount of water is found as the sum of water added to dissolve the salt and the water "stored" within the hydrated salt itself:

$$
\begin{align}
m_\mathrm{tot}(\ce{H2O}) &amp;= m(\ce{H2O})+m_\mathrm{hydr}(\ce{H2O})\\
&amp;= m(\ce{H2O})+n_\mathrm{hydr}(\ce{H2O})\times M(\ce{H2O})\\
&amp;=m(\ce{H2O})+x\times n(\ce{M_pA_q*xH2O})\times M(\ce{H2O})\\
\eqref{eq:2}\quad\Rightarrow\quad&amp;=m(\ce{H2O})+x\times m(\ce{M_pA_q*xH2O})\times \frac{M(\ce{H2O})}{M(\ce{M_pA_q*xH2O})}\label{eq:3}\tag{3}
\end{align}
$$

Now, putting \eqref{eq:2} and \eqref{eq:3} back in \eqref{eq:1}, one can obtain uniform expression for molality of a hydrated salt:

$$b=\frac{m(\ce{M_pA_q*xH2O})}{m(\ce{H2O})\times M(\ce{M_pA_q*xH2O})+x\times m(\ce{M_pA_q*xH2O})\times M(\ce{H2O})}\label{eq:4}\tag{4}$$


   Plugging in the numbers for sodium carbonate decahydrate:
 $$b=\frac{\pu{13.8 g}}{\pu{103.5 g}\times\pu{286.14 g mol-1}+10\times\pu{13.8 g}\times\pu{18.02 g mol-1}}=\pu{4.3E-4mol g-1}$$


A side note regarding the notations and units [1, p. 28]:


  The term molal and the symbol $\pu{m}$ should no longer be used because they are obsolete. One should use instead the term molality of solute $\ce{B}$ and the unit $\pu{mol/kg}$ or an appropriate decimal multiple or submultiple of this unit. (A solution having, for example, a molality of $\pu{1 mol/kg}$ was often called a $1$ molal solution, written $\pu{1 m}$ solution.)


Reference


Thompson, A.; Taylor, B. N. Guide for the Use of the International System of Units (SI). NIST Special Publication 811, 2008.